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{{Short description|Astrophysical phenomena}}
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| image1            = Black hole - Messier 87 crop max res.jpg
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| alt1              = Blackness of space with black marked as centre of donut of orange and red gases
| caption1          = An image of the core region of [[Messier 87]], a [[supermassive black hole]], processed from a sparse array of [[radio telescopes]] known as the [[Event Horizon Telescope|EHT]] with colors indicating [[brightness temperature]].<ref>{{Cite journal |last1=The Event Horizon Telescope Collaboration |last2=Akiyama |first2=Kazunori |last3=Alberdi |first3=Antxon |last4=Alef |first4=Walter |last5=Asada |first5=Keiichi |last6=Azulay |first6=Rebecca |last7=Baczko |first7=Anne-Kathrin |last8=Ball |first8=David |last9=Baloković |first9=Mislav |last10=Barrett |first10=John |last11=Bintley |first11=Dan |last12=Blackburn |first12=Lindy |last13=Boland |first13=Wilfred |last14=Bouman |first14=Katherine L. |last15=Bower |first15=Geoffrey C. |date=2019-04-10 |title=First M87 Event Horizon Telescope Results. IV. Imaging the Central Supermassive Black Hole |journal=The Astrophysical Journal Letters |volume=875 |issue=1 |pages=L4 |doi=10.3847/2041-8213/ab0e85 |doi-access=free |arxiv=1906.11241 |bibcode=2019ApJ...875L...4E |issn=2041-8205}}</ref><ref>{{Cite web |date=2019-04-10 |title=Astronomers capture first image of a black hole |url=https://new.nsf.gov/news/astronomers-capture-first-image-black-hole#image-caption-credit-block |access-date=2025-01-28 |website=new.nsf.gov |language=en}}</ref>

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| caption2          = Simulated view of a [[Schwarzschild black hole]] in front of the [[Large Magellanic Cloud]]. Note the gravitational lensing effect, which produces two enlarged but highly distorted views of the Cloud. Across the top, the [[Milky Way]] disk appears distorted into an arc.<ref name=riazuelo>{{cite journal |author-link= Alain Riazuelo |first= Alain |last= Riazuelo |title= Seeing relativity -- I. Ray tracing in a Schwarzschild metric to explore the maximal analytic extension of the metric and making a proper rendering of the stars |journal= International Journal of Modern Physics D |date= 2019|volume= 28 |issue= 2 |page=1950042 |doi= 10.1142/S0218271819500421 |arxiv= 1511.06025 |bibcode= 2019IJMPD..2850042R |s2cid= 54548877 }}</ref>
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A '''black hole''' is a massive, compact [[astronomical object]] so dense that its gravity prevents anything from escaping, even light. [[Albert Einstein]]'s theory of [[general relativity]] predicts that a sufficiently compact [[mass]] will form a black hole.<ref name="NYT-20150608">{{cite news |last=Overbye |first=Dennis |author-link=Dennis Overbye |title=Black Hole Hunters |url=https://www.nytimes.com/2015/06/09/science/black-hole-event-horizon-telescope.html |date=8 June 2015 |work=[[NASA]] |access-date=8 June 2015 |url-status=live |archive-url=https://web.archive.org/web/20150609023631/http://www.nytimes.com/2015/06/09/science/black-hole-event-horizon-telescope.html |archive-date=9 June 2015}}</ref> The [[boundary (topology)|boundary]] of no escape is called the [[event horizon]]. In general relativity, a black hole’s event horizon seals an object’s fate but produces no locally detectable change when crossed.<ref name ="HamiltonA">{{cite web|author=Hamilton, A.|url=http://jila.colorado.edu/~ajsh/insidebh/schw.html|title=Journey into a Schwarzschild black hole|website=jila.colorado.edu|access-date=28 June 2020|archive-date=3 September 2019|archive-url=https://web.archive.org/web/20190903235853/https://jila.colorado.edu/~ajsh/insidebh/schw.html|url-status=live}}</ref> In many ways, a black hole acts like an ideal [[black body]], as it reflects no light.<ref>{{cite book |title=Gravity from the ground up |first1=Bernard F. |last1=Schutz |author-link1=Bernard F. Schutz |publisher=[[Cambridge University Press]] |date=2003 |isbn=978-0-521-45506-0 |page=110 |url=https://books.google.com/books?id=P_T0xxhDcsIC |url-status=live |archive-url=https://web.archive.org/web/20161202222711/https://books.google.com/books?id=P_T0xxhDcsIC |archive-date=2 December 2016}}</ref><ref>{{cite journal |last=Davies |first=P. C. W. |author-link1=Paul Davies |title=Thermodynamics of Black Holes |url=http://cosmos.asu.edu/publications/papers/ThermodynamicTheoryofBlackHoles%2034.pdf |journal=[[Reports on Progress in Physics]] |volume=41 |date=1978 |issue=8 |pages=1313–1355 |doi=10.1088/0034-4885/41/8/004 |bibcode=1978RPPh...41.1313D|s2cid=250916407 |archive-url=https://web.archive.org/web/20130510184530/http://cosmos.asu.edu/publications/papers/ThermodynamicTheoryofBlackHoles%2034.pdf |archive-date=10 May 2013 }}</ref>  [[Quantum field theory in curved spacetime]] predicts that event horizons emit [[Hawking radiation]], with [[thermal radiation|the same spectrum]] as a black body of a [[temperature]] inversely proportional to its mass. This temperature is of the [[Orders of magnitude (temperature)|order of billionth]]s of a [[kelvin]] for [[stellar black hole]]s, making it essentially impossible to observe directly.

Objects whose [[gravitational field]]s are too strong for light to escape were first considered in the 18th century by [[John Michell]] and [[Pierre-Simon Laplace]]. In 1916, [[Karl Schwarzschild]] found the first modern solution of general relativity that would characterise a black hole. Due to his influential research, the [[Schwarzschild metric]] is named after him. [[David Finkelstein]], in 1958, first published the interpretation of "black hole" as a region of space from which nothing can escape. Black holes were long considered a mathematical curiosity; it was not until the 1960s that theoretical work showed they were a generic prediction of general relativity. The first black hole known was [[Cygnus X-1]], identified by several researchers independently in 1971.<ref name="Webster1972">{{citation | last1=Webster | first1=B. Louise | last2=Murdin | first2=Paul | date=1972 | title=Cygnus&nbsp;X-1—a Spectroscopic Binary with a Heavy Companion? | journal=Nature | volume=235 | issue=5332 | pages=37–38 | doi=10.1038/235037a0 | bibcode = 1972Natur.235...37W | s2cid=4195462 }}</ref><ref name="Bolton1972">{{citation | last=Bolton | first=C. T. | date=1972 | title=Identification of Cygnus&nbsp;X-1 with HDE&nbsp;226868 | journal=Nature | volume=235 | issue=5336 | pages=271–273 | doi=10.1038/235271b0 | bibcode = 1972Natur.235..271B | s2cid=4222070 }}</ref>

Black holes typically form when [[Stellar evolution#Supernova|massive stars collapse]] at the end of their [[Stellar evolution|life cycle]]. After a black hole has formed, it can grow by absorbing mass from its surroundings. Supermassive black holes of millions of [[Solar mass|solar masses]] may form by absorbing other stars and merging with other black holes, or via [[Direct collapse black hole|direct collapse]] of [[gas cloud]]s. There is consensus that [[supermassive black hole]]s exist in the centres of most [[galaxies]].

The presence of a black hole can be inferred through its interaction with other [[matter]] and with electromagnetic radiation such as visible light. Matter falling toward a black hole can form an [[accretion disk]] of infalling plasma, heated by [[friction]] and emitting light. In extreme cases, this creates a [[quasar]], some of the brightest objects in the universe. Stars passing too close to a supermassive black hole can be shredded into streamers that shine very brightly before being "swallowed."<ref name="pmid32001633">{{cite journal | author=Clery D | title=Black holes caught in the act of swallowing stars | journal=[[Science (journal)|Science]] | volume=367 | issue=6477 | page=495 | year=2020 | doi = 10.1126/science.367.6477.495 | pmid=32001633| bibcode=2020Sci...367..495C| s2cid=210984462 }}</ref> If other stars are orbiting a black hole, their orbits can be used to determine the black hole's mass and location. Such observations can be used to exclude possible alternatives such as [[neutron star]]s. In this way, astronomers have identified numerous stellar black hole candidates in [[binary star|binary systems]] and established that the radio source known as [[Sagittarius A*]], at the core of the [[Milky Way]] galaxy, contains a supermassive black hole of about 4.3&nbsp;million [[Solar energy|solar]] masses.

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== History ==
The idea of a body so big that even light could not escape was briefly proposed by English astronomical pioneer and clergyman [[John Michell]] and independently by French scientist [[Pierre-Simon Laplace]]. Both scholars proposed very large stars rather than the modern model of stars with extraordinary density.<ref name="origin">{{cite journal|last1=Montgomery|first1=Colin|last2=Orchiston|first2=Wayne|last3=Whittingham|first3=Ian|year=2009|title=Michell, Laplace and the origin of the black hole concept|journal=Journal of Astronomical History and Heritage|volume=12|issue=2|pages=90–96|doi=10.3724/SP.J.1440-2807.2009.02.01 |bibcode=2009JAHH...12...90M|s2cid=55890996 |url=https://researchonline.jcu.edu.au/9892/1/Microsoft_Word_-_Paper__Black_Hole_Concept_Final_.pdf }}</ref>

Michell's idea, in a short part of a letter published in 1784, calculated that a star with the same density but 500 times the radius of the sun would not let any emitted light escape; the surface [[escape velocity]] would exceed the speed of light. Michell correctly noted that such supermassive but non-radiating bodies might be detectable through their gravitational effects on nearby visible bodies.<ref name="origin" /><ref>{{Cite journal |last=Michell |first=J. |author-link1=John Michell |date=1784 |title=On the Means of Discovering the Distance, Magnitude, &c. of the Fixed Stars, in Consequence of the Diminution of the Velocity of Their Light, in Case Such a Diminution Should be Found to Take Place in any of Them, and Such Other Data Should be Procured from Observations, as Would be Farther Necessary for That Purpose |journal=[[Philosophical Transactions of the Royal Society]] |volume=74 |pages=35–57 |bibcode=1784RSPT...74...35M |doi=10.1098/rstl.1784.0008|jstor=106576|doi-access=free}}</ref><ref name=thorne_123_124>{{harvnb|Thorne|1994|pp=123–124}}</ref>

In 1796, Laplace mentioned that a star could be invisible if it were sufficiently large while speculating on the origin of the Solar System in his book ''Exposition du Système du Monde.'' [[Franz Xaver von Zach]] asked Laplace for a mathematical analysis, which Laplace provided and published in journal edited by von Zach.<ref name="origin"/>

Scholars of the time were initially excited by the proposal that giant but invisible 'dark stars' might be hiding in plain view, but enthusiasm dampened when the wavelike nature of light became apparent in the early nineteenth century,<ref>{{cite book |title=Light and Electron Microscopy |first1=Elizabeth M. |last1=Slayter |first2=Henry S. |last2=Slayter |publisher=[[Cambridge University Press]] |year=1992 |isbn=978-0-521-33948-3 |url=https://books.google.com/books?id=LlePVS9oq7MC |url-status=live |archive-url=https://web.archive.org/web/20171130151044/https://books.google.com/books?id=LlePVS9oq7MC |archive-date=30 November 2017}}</ref> since light was understood as a wave rather than a particle, it was unclear what, if any, influence gravity would have on escaping light waves.<ref name=origin /><ref name=thorne_123_124 />

=== General relativity ===
{{See also|History of general relativity}}
{{General relativity sidebar|phenomena}}

In 1915, [[Albert Einstein]] developed his theory of [[general relativity]], having earlier shown that gravity does influence light's motion. Only a few months later, [[Karl Schwarzschild]] found a [[Schwarzschild metric|solution]] to the [[Einstein field equations]] that describes the [[gravitational field]] of a [[point mass]] and a spherical mass.<ref name="Levy">{{cite journal |last1=Levy |first1=Adam |title=How black holes morphed from theory to reality |journal=Knowable Magazine |date=11 January 2021 |doi=10.1146/knowable-010921-1 |doi-access=free |url=https://knowablemagazine.org/article/physical-world/2021/how-black-holes-morphed-theory-reality |access-date=25 March 2022|url-access=subscription }}</ref><ref name="Schwarzschild1916">{{Cite journal |last=Schwarzschild |first=K. |author-link1=Karl Schwarzschild |date=1916 |title=Über das Gravitationsfeld eines Massenpunktes nach der Einsteinschen Theorie |url=https://archive.org/stream/sitzungsberichte1916deutsch#page/188/mode/2up |journal=Sitzungsberichte der Königlich Preussischen Akademie der Wissenschaften |volume=7 |pages=189–196|bibcode=1916SPAW.......189S}}
:* Translation: {{cite arXiv |last1=Antoci |first1=S. |last2=Loinger |first2=A. |year=1999 |title=On the gravitational field of a mass point according to Einstein's theory |eprint=physics/9905030 }} and {{Cite journal |last=Schwarzschild |first=K. |author-link1=Karl Schwarzschild |date=1916 |title=Über das Gravitationsfeld einer Kugel aus inkompressibler Flüssigkeit nach der Einsteinschen Theorie |url=https://archive.org/stream/sitzungsberichte1916deutsch#page/424/mode/2up |journal=Sitzungsberichte der Königlich Preussischen Akademie der Wissenschaften |volume=18 |pages=424–434|bibcode=1916skpa.conf..424S}}
:* Translation: {{cite arXiv |last1=Antoci |first1=S. |year=1999 |title=On the gravitational field of a sphere of incompressible fluid according to Einstein's theory |eprint=physics/9912033 }}</ref> A few months after Schwarzschild, [[Johannes Droste]], a student of [[Hendrik Lorentz]], independently gave the same solution for the point mass and wrote more extensively about its properties.<ref>{{Cite journal |last=Droste |first=J. |title=On the field of a single centre in Einstein's theory of gravitation, and the motion of a particle in that field |journal=Proceedings Royal Academy Amsterdam |date=1917 |volume=19 |issue=1 |pages=197–215 |url=http://www.dwc.knaw.nl/DL/publications/PU00012325.pdf|archive-url=https://web.archive.org/web/20130518034708/http://www.dwc.knaw.nl/DL/publications/PU00012325.pdf |archive-date=18 May 2013 |access-date=16 September 2012 }}</ref><ref>{{cite book |title=Studies in the history of general relativity |editor1-last=Eisenstaedt |editor1-first=Jean |editor2-last=Kox |editor2-first=A. J. |isbn=978-0-8176-3479-7 |date=1992 |publisher=Birkhäuser |chapter=General Relativity in the Netherlands: 1915–1920 |last=Kox |first=A. J. |chapter-url=https://books.google.com/books?id=vDHCF_3vIhUC&pg=PA41 |page=41 |access-date=23 February 2016 |archive-date=10 August 2016 |archive-url=https://web.archive.org/web/20160810215219/https://books.google.com/books?id=vDHCF_3vIhUC&pg=PA41 |url-status=live }}</ref> This solution had a peculiar behaviour at what is now called the [[Schwarzschild radius]], where it became [[singularity (mathematics)|singular]], meaning that some of the terms in the Einstein equations became infinite. The nature of this surface was not quite understood at the time.

In 1924, [[Arthur Eddington]] showed that the singularity disappeared after a change of coordinates. In 1933, [[Georges Lemaître]] realised that this meant the singularity at the Schwarzschild radius was a non-physical [[coordinate singularity]].<ref name="HooftHist">{{Cite web |last='t Hooft |first=G. |author-link1=Gerard 't Hooft |date=2009 |title=Introduction to the Theory of Black Holes |url=http://www.phys.uu.nl/~thooft/lectures/blackholes/BH_lecturenotes.pdf |publisher=Institute for Theoretical Physics / Spinoza Institute |pages=47–48|archive-url=https://web.archive.org/web/20090521082736/http://www.phys.uu.nl/~thooft/lectures/blackholes/BH_lecturenotes.pdf |archive-date=21 May 2009 |access-date=24 June 2010 }}</ref> Arthur Eddington commented on the possibility of a star with mass compressed to the Schwarzschild radius in a 1926 book, noting that Einstein's theory allows us to rule out overly large densities for visible stars like [[Betelgeuse]] because "a star of 250 million km radius could not possibly have so high a density as the Sun. Firstly, the force of gravitation would be so great that light would be unable to escape from it, the rays falling back to the star like a stone to the earth. Secondly, the red shift of the spectral lines would be so great that the spectrum would be shifted out of existence. Thirdly, the mass would produce so much curvature of the spacetime metric that space would close up around the star, leaving us outside (i.e., nowhere)."<ref name="eddington1926">{{cite book |first=Arthur |last=Eddington |author-link=Arthur Eddington |date=1926 |title=The Internal Constitution of the Stars |series=Science |volume=52 |issue=1341 |pages=233–40 |url=https://books.google.com/books?id=RjC9DpnWFbkC&pg=PA6 |publisher=Cambridge University Press |isbn=978-0-521-33708-3 |url-status=live |archive-url=https://web.archive.org/web/20160811034409/https://books.google.com/books?id=RjC9DpnWFbkC&lpg=PP1&pg=PA6 |archive-date=11 August 2016 |pmid=17747682 |doi=10.1126/science.52.1341.233|bibcode=1920Sci....52..233E }}</ref><ref>{{cite book |last1=Thorne |first1=Kip S. |url=https://archive.org/details/blackholestimewa0000thor |title=Black Holes and Time Warps: Einstein's Outrageous Legacy |last2=Hawking |first2=Stephen |date=1994 |publisher=W. W. Norton & Company |isbn=978-0-393-31276-8 |editor-last=Agrawal |editor-first=Milan |edition=1st |pages=[https://archive.org/details/blackholestimewa0000thor/page/134 134]–135 |quote=The first conclusion was the Newtonian version of light not escaping; the second was a semi-accurate, relativistic description; and the third was typical Eddingtonian hyperbole{{nbsp}}... when a star is as small as the critical circumference, the curvature is strong but not infinite, and space is definitely not wrapped around the star. Eddington may have known this, but his description made a good story, and it captured in a whimsical way the spirit of Schwarzschild's spacetime curvature." |access-date=12 April 2019 |url-access=registration}}</ref>

In 1931, [[Subrahmanyan Chandrasekhar]] calculated, using special relativity, that a non-rotating body of [[electron-degenerate matter]] above a certain limiting mass (now called the [[Chandrasekhar limit]] at {{Solar mass|1.4}}) has no stable solutions.<ref name="venkataraman92">{{cite book |first=G. |last=Venkataraman |title=Chandrasekhar and his limit |page=89 |publisher=Universities Press |date=1992 |url=https://books.google.com/books?id=HNSdDFOJ4wkC&pg=PA89 |isbn=978-81-7371-035-3 |url-status=live |archive-url=https://web.archive.org/web/20160811035848/https://books.google.com/books?id=HNSdDFOJ4wkC&pg=PA89 |archive-date=11 August 2016}}</ref> His arguments were opposed by many of his contemporaries like Eddington and [[Lev Landau]], who argued that some yet unknown mechanism would stop the collapse.<ref>{{Cite journal |last=Detweiler |first=S. |date=1981 |title=Resource letter BH-1: Black holes |journal=[[American Journal of Physics]] |volume=49 |issue=5 |pages=394–400 |doi=10.1119/1.12686|bibcode=1981AmJPh..49..394D}}</ref> They were partly correct: a [[white dwarf]] slightly more massive than the Chandrasekhar limit will collapse into a [[neutron star]],<ref>{{cite book |last1=Harpaz |first1=A. |date=1994 |title=Stellar evolution |url=https://books.google.com/books?id=kd4VEZv8oo0C&pg=PA105 |publisher=[[A K Peters, Ltd.|A K Peters]] |page=105 |isbn=978-1-56881-012-6 |url-status=live |archive-url=https://web.archive.org/web/20160811025449/https://books.google.com/books?id=kd4VEZv8oo0C&pg=PA105 |archive-date=11 August 2016}}</ref> which is itself stable.

In 1939, [[Robert Oppenheimer]] and [[George Volkoff]] predicted that neutron stars above another limit, the [[Tolman–Oppenheimer–Volkoff limit]], would collapse further for the reasons presented by Chandrasekhar, and concluded that no law of physics was likely to intervene and stop at least some stars from collapsing to black holes.<ref name="OV1939">{{Cite journal |last1=Oppenheimer |first1=J. R. |author-link1=J. Robert Oppenheimer |last2=Volkoff |first2=G. M. |author-link2=George Volkoff |date=1939 |title=On Massive Neutron Cores |journal=[[Physical Review]] |volume=55 |issue=4 |pages=374–381 |doi=10.1103/PhysRev.55.374|bibcode=1939PhRv...55..374O}}</ref> Their original calculations, based on the [[Pauli exclusion principle]], gave it as {{Solar mass|0.7}}. Subsequent consideration of neutron-neutron repulsion mediated by the strong force raised the estimate to approximately {{Solar mass|1.5}} to {{Solar mass|3.0}}.<ref name="Bombaci">{{cite journal |first=I. |last=Bombaci |date=1996 |title=The Maximum Mass of a Neutron Star |journal=[[Astronomy and Astrophysics]] |volume=305 |pages=871–877 |bibcode=1996A&A...305..871B}}</ref> Observations of the neutron star merger [[GW170817]], which is thought to have generated a black hole shortly afterward, have refined the TOV limit estimate to ~{{Solar mass|2.17}}.<ref name="Cho2018">{{cite journal |last=Cho |first=A. |title=A weight limit emerges for neutron stars |journal=Science |volume=359 |issue=6377 |pages=724–725 |date=16 February 2018 |doi=10.1126/science.359.6377.724 |pmid=29449468 |bibcode=2018Sci...359..724C}}</ref><ref name="Margalit2017">{{cite journal |last1=Margalit |first1=B. |last2=Metzger |first2=B. D. |title=Constraining the Maximum Mass of Neutron Stars from Multi-messenger Observations of GW170817 |journal=The Astrophysical Journal |volume=850 |issue=2 |date=1 December 2017 |page=L19 |doi=10.3847/2041-8213/aa991c |arxiv=1710.05938 |bibcode=2017ApJ...850L..19M|s2cid=119342447 |doi-access=free }}</ref><ref name="Shibata2017">{{cite journal |last1=Shibata |first1=M. |last2=Fujibayashi |first2=S. |last3=Hotokezaka |first3=K. |last4=Kiuchi |first4=K. |last5=Kyutoku |first5=K. |last6=Sekiguchi |first6=Y. |last7=Tanaka |first7=M. |title=Modeling GW170817 based on numerical relativity and its implications |journal=Physical Review D |volume=96 |issue=12 |page=123012 |date=22 December 2017 |doi=10.1103/PhysRevD.96.123012 |arxiv=1710.07579 |bibcode=2017PhRvD..96l3012S|s2cid=119206732 }}</ref><ref name="Ruiz2018">{{cite journal |last1=Ruiz |first1=M. |last2=Shapiro |first2=S. L. |last3=Tsokaros |first3=A. |title=GW170817, general relativistic magnetohydrodynamic simulations, and the neutron star maximum mass |journal=Physical Review D |volume=97 |issue=2 |page=021501 |date=11 January 2018 |doi=10.1103/PhysRevD.97.021501 |pmid=30003183 |pmc=6036631 |arxiv=1711.00473 |bibcode=2018PhRvD..97b1501R}}</ref><ref name="Rezzolla2018">{{cite journal |last1=Rezzolla |first1=L. |last2=Most |first2=E. R. |last3=Weih |first3=L. R. |title=Using Gravitational-wave Observations and Quasi-universal Relations to Constrain the Maximum Mass of Neutron Stars |journal=Astrophysical Journal |volume=852 |issue=2 |date=9 January 2018 |page=L25 |doi=10.3847/2041-8213/aaa401 |arxiv=1711.00314 |bibcode=2018ApJ...852L..25R|s2cid=119359694 |doi-access=free }}</ref>

Oppenheimer and his co-authors interpreted the singularity at the boundary of the Schwarzschild radius as indicating that this was the boundary of a bubble in which time stopped.  This is a valid point of view for external observers, but not for infalling observers.  The hypothetical collapsed stars were called "frozen stars", because an outside observer would see the surface of the star frozen in time at the instant where its collapse takes it to the Schwarzschild radius.<ref name=Ruffini-2011>{{Cite journal |last1=Ruffini |first1=R. |author-link1=Remo Ruffini |last2=Wheeler |first2=J. A. |author-link2=John Archibald Wheeler |date=1971 |title=Introducing the black hole |url=http://authors.library.caltech.edu/14972/1/Ruffini2009p1645Phys_Today.pdf |journal=[[Physics Today]] |volume=24 |issue=1 |pages=30–41 |doi=10.1063/1.3022513|bibcode=1971PhT....24a..30R |archive-url=https://web.archive.org/web/20110725133758/http://authors.library.caltech.edu/14972/1/Ruffini2009p1645Phys_Today.pdf |archive-date=25 July 2011 |access-date=5 December 2009 }}</ref>

Also in 1939, Einstein attempted to prove that black holes were impossible in his publication "On a Stationary System with Spherical Symmetry Consisting of Many Gravitating Masses", using his theory of general relativity to defend his argument.<ref name="Bernstein-2007">{{Cite journal |last=Bernstein |first=Jeremy |title=The Reluctant Father of Black Holes |url=https://www.scientificamerican.com/article/the-reluctant-father-of-black-holes-2007-04/ |access-date=3 August 2023 |journal=[[Scientific American]] |date=2007 |volume=17 |pages=4–11 |doi=10.1038/scientificamerican0407-4sp |language=en|url-access=subscription }}</ref> Months later, Oppenheimer and his student [[Hartland Snyder]] provided the [[Oppenheimer–Snyder model]] in their paper "On Continued Gravitational Contraction",<ref>{{cite journal |last1=Oppenheimer |first1=J.R. |last2=Snyder |first2=H. |author-link2=Hartland Snyder |year=1939 |title=On Continued Gravitational Contraction |journal=[[Physical Review]] |volume=56 |issue=5 |pages=455–459 |bibcode=1939PhRv...56..455O |doi=10.1103/PhysRev.56.455 |doi-access=free}}</ref> which predicted the existence of black holes. In the paper, which made no reference to Einstein's recent publication, Oppenheimer and Snyder used Einstein's own theory of general relativity to show the conditions on how a black hole could develop, for the first time in contemporary physics.<ref name="Bernstein-2007" />

In 1958, [[David Finkelstein]] identified the Schwarzschild surface as an event horizon, "a perfect unidirectional membrane: causal influences can cross it in only one direction".<ref>{{Cite journal |last=Finkelstein |first=D. |author-link1=David Finkelstein |date=1958 |title=Past-Future Asymmetry of the Gravitational Field of a Point Particle |journal=[[Physical Review]] |volume=110 |issue=4 |pages=965–967 |doi=10.1103/PhysRev.110.965|bibcode=1958PhRv..110..965F}}</ref> Finkelstein created a new reference frame to include the point of view of infalling observers.<ref name=Bartusiak/>{{rp|103}} Finkelstein's solution extended the Schwarzschild solution for the future of observers falling into a black hole.  A similar concept had already been found by [[Martin Kruskal]] but Wheeler had not understood its significance.<ref name=Bartusiak/>{{rp|103}} Eventually the [[Kruskal–Szekeres coordinates]] helped physics understand black holes from multiple perspectives.<ref name=Ruffini-2011/><ref>{{cite journal |last1=Kruskal |first1=M. |author-link1=Martin Kruskal |date=1960 |title=Maximal Extension of Schwarzschild Metric |journal=[[Physical Review]] |volume=119 |issue=5 |page=1743 |doi=10.1103/PhysRev.119.1743 |bibcode=1960PhRv..119.1743K}}</ref>

=== Golden age ===
[[File:BH-JPL-A&A1979.jpg |thumb|The first simulated image of a black hole, created by [[Jean-Pierre Luminet]] in 1978 and featuring the characteristic shadow, [[photon sphere]], and [[gravitational lensing|lensed]] [[accretion disk]]. The disk is brighter on one side due to the [[Doppler beaming]].<ref>{{Cite journal |last=Luminet |first=J.-P. |date=May 1979 |title=Image of a spherical black hole with thin accretion disk. |url=https://ui.adsabs.harvard.edu/abs/1979A&A....75..228L/abstract |journal=Astronomy and Astrophysics |language=en |volume=75 |pages=228–235 |bibcode=1979A&A....75..228L |issn=0004-6361}}</ref><ref>{{cite web |author=French National Centre for Scientific Research |title=First ever image of a black hole: a CNRS researcher had simulated it as early as 1979 |url=https://www.cnrs.fr/en/press/first-ever-image-black-hole-cnrs-researcher-had-simulated-it-early-1979 |website=CNRS |date=10 April 2019 |access-date=18 June 2025}}</ref>]]
The era from the mid-1960s to the mid-1970s was the "golden age of black hole research", when general relativity and black holes became mainstream subjects of research.<ref>{{cite book |title=The future of theoretical physics and cosmology: celebrating Stephen Hawking's 60th birthday |chapter=Warping spacetime |first1=Kip |last1=Thorne |publisher=Cambridge University Press |year=2003 |isbn=0-521-82081-2 |page=74 |url=https://books.google.com/books?id=yLy4b61rfPwC}} [https://books.google.com/books?id=yLy4b61rfPwC&pg=PA74 Extract of page 74]</ref><ref>{{Cite book |last=Thorne |first=Kip |title=Black Holes and Time Warps: Einstein's Outrageous Legacy (Commonwealth Fund Book Program) |date=1995 |publisher=W. W. Norton & Company, Incorporated |isbn=978-0-393-31276-8 |edition=1 |series=Commonwealth Fund Book Program Series |location=Erscheinungsort nicht ermittelbar}}</ref>{{rp|p=258}} 

In this period more general black hole solutions were found. In 1963, [[Roy Kerr]] found [[Kerr metric|the exact solution]] for a [[rotating black hole]]. Two years later, [[Ezra T. Newman|Ezra Newman]] found the [[axisymmetric]] solution for a black hole that is both rotating and [[electrically charged]].<ref>{{Cite journal |last1=Newman |first1=E. T. |author-link1=Ezra T. Newman |last2=Couch |first2=E. |last3=Chinnapared |first3=K. |last4=Exton |first4=A. |last5=Prakash |first5=A. |last6=Torrence |first6=R. |display-authors=1 |date=1965 |title=Metric of a Rotating, Charged Mass |journal=[[Journal of Mathematical Physics]] |volume=6 |issue=6 |page=918 |doi=10.1063/1.1704351 |bibcode=1965JMP.....6..918N}}</ref> Through the work of [[Werner Israel]],<ref>{{cite journal |last=Israel |first=W. |date=1967 |title=Event Horizons in Static Vacuum Space-Times |journal=[[Physical Review]] |volume=164 |issue=5 |page=1776 |doi=10.1103/PhysRev.164.1776 |bibcode=1967PhRv..164.1776I}}</ref> [[Brandon Carter]],<ref>{{cite journal |last=Carter |first=B. |author-link1=Brandon Carter |date=1971 |title=Axisymmetric Black Hole Has Only Two Degrees of Freedom |journal=[[Physical Review Letters]] |volume=26 |issue=6 |page=331 |doi=10.1103/PhysRevLett.26.331 |bibcode=1971PhRvL..26..331C}}</ref><ref>{{cite book |last=Carter |first=B. |author-link1=Brandon Carter |date=1977 |chapter=The vacuum black hole uniqueness theorem and its conceivable generalisations |title=Proceedings of the 1st Marcel Grossmann meeting on general relativity |pages=243–254 }}</ref> and David Robinson<ref>{{cite journal |last1=Robinson |first1=D. |date=1975 |title=Uniqueness of the Kerr Black Hole |journal=[[Physical Review Letters]] |volume=34 |issue=14 |page=905 |doi=10.1103/PhysRevLett.34.905 |bibcode=1975PhRvL..34..905R}}</ref> the [[no-hair theorem]] emerged, stating that a stationary black hole solution is completely described by the three parameters of the [[Kerr–Newman metric]]: [[mass]], [[angular momentum]], and electric charge.<ref name="HeuslerNoHair" />

At first, it was suspected that the strange features of the black hole solutions were pathological artefacts from the symmetry conditions imposed, and that the singularities would not appear in generic situations. This view was held in particular by [[Vladimir A. Belinsky|Vladimir Belinsky]], [[Isaak Markovich Khalatnikov|Isaak Khalatnikov]], and [[Evgeny Lifshitz]], who tried to prove that no singularities appear in generic solutions. However, in the late 1960s [[Roger Penrose]]<ref name="penrose1965">{{cite journal |last1=Penrose |first1=R. |author-link1=Roger Penrose |date=1965 |title=Gravitational Collapse and Space-Time Singularities |journal=[[Physical Review Letters]] |volume=14 |issue=3 |page=57 |doi=10.1103/PhysRevLett.14.57 |bibcode=1965PhRvL..14...57P |s2cid=116755736|url=http://pdfs.semanticscholar.org/faad/1f4358fddf70df2e00c0a290b7e4501c27de.pdf |archive-url=https://web.archive.org/web/20201011221750/http://pdfs.semanticscholar.org/faad/1f4358fddf70df2e00c0a290b7e4501c27de.pdf |archive-date=11 October 2020 }}</ref> and [[Stephen Hawking]] used global techniques to prove that singularities appear generically.<ref>{{cite journal |last1=Ford |first1=L. H. |date=2003 |title=The Classical Singularity Theorems and Their Quantum Loopholes |journal=[[International Journal of Theoretical Physics]] |volume=42 |issue=6 |pages=1219–1227 |doi=10.1023/A:1025754515197 |arxiv=gr-qc/0301045 |bibcode=2003gr.qc.....1045F |s2cid=14404560}}</ref> For this work, Penrose received half of the 2020 [[Nobel Prize in Physics]], Hawking having died in 2018.<ref>{{Cite web|title=The Nobel Prize in Physics 2020|url=https://www.nobelprize.org/prizes/physics/2020/summary/|access-date=8 October 2020|website=NobelPrize.org|archive-date=24 April 2021|archive-url=https://web.archive.org/web/20210424115309/https://www.nobelprize.org/prizes/physics/2020/summary/|url-status=live}}</ref>

Astronomical observations also made great strides during this era. In 1967 [[Antony Hewish]] and [[Jocelyn Bell Burnell]] discovered [[pulsar]]s<ref>{{Cite journal |last1=Hewish |first1=A. |author-link1=Antony Hewish |last2=Bell |first2=S. J. |author-link2=Jocelyn Bell Burnell |last3=Pilkington |first3=J. D. H. |last4=Scott |first4=P. F. |last5=Collins |first5=R. A. |display-authors=1 |date=1968 |title=Observation of a Rapidly Pulsating Radio Source |journal=[[Nature (journal)|Nature]] |volume=217 |issue=5130 |pages=709–713 |doi=10.1038/217709a0|bibcode=1968Natur.217..709H|s2cid=4277613 }}</ref><ref>{{Cite journal |last1=Pilkington |first1=J. D. H. |last2=Hewish |first2=A. |author-link2=Antony Hewish |last3=Bell |first3=S. J. |author-link3=Jocelyn Bell Burnell |last4=Cole |first4=T. W. |display-authors=1 |date=1968 |title=Observations of some further Pulsed Radio Sources |journal=[[Nature (journal)|Nature]] |volume=218 |issue=5137 |pages=126–129 |doi=10.1038/218126a0|bibcode=1968Natur.218..126P|s2cid=4253103 }}</ref> and by 1969, these were shown to be rapidly rotating neutron stars.<ref name="araa8_265">{{cite journal |last=Hewish |first=A. |author-link1=Antony Hewish |date=1970 |title=Pulsars |journal=[[Annual Review of Astronomy and Astrophysics]] |volume=8 |issue=1 |pages=265–296 |bibcode=1970ARA&A...8..265H |doi=10.1146/annurev.aa.08.090170.001405}}</ref> Until that time, neutron stars, like black holes, were regarded as just theoretical curiosities; but the discovery of pulsars showed their physical relevance and spurred a further interest in all types of compact objects that might be formed by gravitational collapse.<ref>{{Cite web |url=https://www.smithsonianmag.com/science-nature/Fifty-years-ago-grad-students-discovery-changed-course-astrophysics-180968288/ |title=Fifty Years Ago, a Grad Student's Discovery Changed the Course of Astrophysics |date=28 February 2018 |access-date=22 December 2023 |website=Smithsonian Magazine |last=Boissoneault |first=Lorraine}}</ref>
Based on observations in [[Royal Greenwich Observatory|Greenwich]] and [[David Dunlap Observatory|Toronto]] in the early 1970s, [[Cygnus X-1]], a galactic [[X-ray]] source discovered in 1964, became the first astronomical object commonly accepted to be a black hole.<ref>{{citation | last=Rolston | first=Bruce | date=10 November 1997 | url=http://news.utoronto.ca/bin/bulletin/nov10_97/art4.htm | title=The First Black Hole | publisher=University of Toronto | access-date=11 March 2008 | archive-url = https://web.archive.org/web/20080307181205/http://www.news.utoronto.ca/bin/bulletin/nov10_97/art4.htm | archive-date = 7 March 2008 }}</ref><ref name="Shipman1975">{{citation | last1=Shipman | first1=H. L. | date=1975 | title=The implausible history of triple star models for Cygnus&nbsp;X-1 Evidence for a black hole | journal=Astrophysical Letters | volume=16 | issue=1 | pages=9–12 | bibcode=1975ApL....16....9S | doi=10.1016/S0304-8853(99)00384-4 | last2=Yu | first2=Z | last3=Du | first3=Y.W }}</ref>

Work by [[James Bardeen]], [[Jacob Bekenstein]], Carter, and Hawking in the early 1970s led to the formulation of [[black hole thermodynamics]].<ref>{{Cite journal |last1=Bardeen |first1=J. M. |author-link1=James M. Bardeen |last2=Carter |first2=B. |author-link2=Brandon Carter |last3=Hawking |first3=S. W. |author-link3=Stephen Hawking |date=1973 |title=The four laws of black hole mechanics |journal=[[Communications in Mathematical Physics]] |volume=31 |issue=2 |pages=161–170 |doi=10.1007/BF01645742 |mr=0334798 |zbl=1125.83309 |bibcode=1973CMaPh..31..161B |s2cid=54690354 |url=http://projecteuclid.org/euclid.cmp/1103858973 |access-date=4 June 2021 |archive-date=16 May 2020 |archive-url=https://web.archive.org/web/20200516211604/https://projecteuclid.org/euclid.cmp/1103858973 |url-status=live }}</ref> These laws describe the behaviour of a black hole in close analogy to the [[laws of thermodynamics]] by relating mass to energy, area to [[entropy]], and [[surface gravity]] to [[temperature]]. The analogy was completed when Hawking, in 1974, showed that [[quantum field theory]] implies that black holes should radiate like a [[black body]] with a temperature proportional to the surface gravity of the black hole, predicting the effect now known as [[Hawking radiation]].<ref name=Hawking1974 />

=== Observation ===
[[File:Black hole optics.png|thumb|An infographic explaining in detail the appearance of a black hole.]]
On 11 February 2016, the [[LIGO Scientific Collaboration]] and the [[Virgo interferometer|Virgo collaboration]] [[first observation of gravitational waves|announced the first direct detection]] of [[gravitational wave]]s, representing the first observation of a black hole merger.<ref name="PRL-20160211" /> On 10 April 2019, the first direct image of a black hole and its vicinity was published, following observations made by the [[Event Horizon Telescope]] (EHT) in 2017 of the supermassive black hole in Messier 87's [[Galactic Center|galactic centre]].<ref name="APJL-20190410">{{cite journal|last1=Event Horizon Telescope|first1=The|author-link1=Event Horizon Telescope|date=2019|title=First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole|journal=[[The Astrophysical Journal]]|volume=875|page=L1|arxiv=1906.11238|bibcode=2019ApJ...875L...1E|doi=10.3847/2041-8213/ab0ec7|number=1|s2cid=145906806 |doi-access=free }}</ref><ref name="BoumanJohnson2016">{{cite book |last1=Bouman |first1=Katherine L. |title=2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) |author-link1=Katie Bouman |last2=Johnson |first2=Michael D. |last3=Zoran |first3=Daniel |last4=Fish |first4=Vincent L. |last5=Doeleman |first5=Sheperd S. |last6=Freeman |first6=William T. |chapter=Computational Imaging for VLBI Image Reconstruction |year=2016 |pages=913–922 |doi=10.1109/CVPR.2016.105 |hdl=1721.1/103077 |arxiv=1512.01413|isbn=978-1-4673-8851-1|s2cid=9085016 }}</ref><ref name="NYT-20190412">{{cite news |last=Gardiner |first=Aidan |title=When a Black Hole Finally Reveals Itself, It Helps to Have Our Very Own Cosmic Reporter – Astronomers announced Wednesday that they had captured the first image of a black hole. The Times's Dennis Overbye answers readers' questions.|url=https://www.nytimes.com/2019/04/12/reader-center/black-holes-dennis-overbye.html |archive-url=https://ghostarchive.org/archive/20220101/https://www.nytimes.com/2019/04/12/reader-center/black-holes-dennis-overbye.html |archive-date=1 January 2022 |url-access=limited |date=12 April 2018 |work=[[The New York Times]] |access-date=15 April 2019}}{{cbignore}}</ref>  [[Gaia (spacecraft)|Gaia mission]] observations have found evidence of a Sun-like star orbiting a black hole named [[Gaia BH1]] around {{Convert|1,560|ly|pc|lk=on|abbr=off}} away;<ref name="El-Badry">{{Cite journal |last1=El-Badry |first1=Kareem |last2=Rix |first2=Hans-Walter |last3=Quataert |first3=Eliot |last4=Howard |first4=Andrew W. |last5=Isaacson |first5=Howard |last6=Fuller |first6=Jim |last7=Hawkins |first7=Keith |last8=Breivik |first8=Katelyn |last9=Wong |first9=Kaze W. K. |last10=Rodriguez |first10=Antonio C. |last11=Conroy |first11=Charlie |last12=Shahaf |first12=Sahar |last13=Mazeh |first13=Tsevi |last14=Arenou |first14=Frédéric |last15=Burdge |first15=Kevin B. |last16=Bashi |first16=Dolev |last17=Faigler |first17=Simchon |last18=Weisz |first18=Daniel R. |last19=Seeburger |first19=Rhys |last20=Monter |first20=Silvia Almada |last21=Wojno |first21=Jennifer |title=A Sun-like star orbiting a black hole  |journal=Monthly Notices of the Royal Astronomical Society |year=2023 |volume=518 |pages=1057–1085 |doi=10.1093/mnras/stac3140 |doi-access=free |arxiv=2209.06833 }}</ref> evidence suggests a [[brown dwarf star]] orbits [[Gaia BH2]].<ref>{{Cite journal |last1=Marchant |first1=Pablo |last2=Bodensteiner |first2=Julia |date=September 2024 |title=The Evolution of Massive Binary Stars |journal=Annual Review of Astronomy and Astrophysics |language=en |volume=62 |issue=1 |pages=21–61 |doi=10.1146/annurev-astro-052722-105936 |doi-access=free |issn=0066-4146|arxiv=2311.01865 |bibcode=2024ARA&A..62...21M }}</ref> Though only a couple dozen black holes have been found so far in the Milky Way, there are thought to be hundreds of millions, most of which are solitary and do not cause emission of radiation.<ref>{{cite web |title=ESO Instrument Finds Closest Black Hole to Earth |url=https://www.eso.org/public/news/eso2007/ |publisher=[[European Southern Observatory]] |date=6 May 2020 |access-date=2 April 2021 |archive-date=6 May 2020 |archive-url=https://web.archive.org/web/20200506232455/https://www.eso.org/public/news/eso2007/ |url-status=live }}</ref> Therefore, they would only be detectable by [[gravitational lens]]ing.

=== Etymology ===

In December 1967, a student reportedly suggested the phrase "black hole" at a lecture by [[John Archibald Wheeler|John Wheeler]]; Wheeler adopted the term for its brevity and "advertising value", and Wheeler's stature in the field ensured it quickly caught on.<ref name=Bartusiak/><ref>{{cite news |title=Pioneering Physicist John Wheeler Dies at 96 |url=https://www.scientificamerican.com/article/pioneering-physicist-john-wheeler-dies/ |access-date=27 November 2016 |work=[[Scientific American]] |url-status=live |archive-url=https://web.archive.org/web/20161128050759/https://www.scientificamerican.com/article/pioneering-physicist-john-wheeler-dies/ |archive-date=28 November 2016}}</ref> leading some to credit Wheeler with coining the phrase.<ref>{{cite news |last1=Overbye |first1=Dennis |title=John A. Wheeler, Physicist Who Coined the Term 'Black Hole,' Is Dead at 96 |url=https://www.nytimes.com/2008/04/14/science/14wheeler.html |access-date=27 November 2016 |work=[[The New York Times]] |date=14 April 2008 |url-status=live |archive-url=https://web.archive.org/web/20161122210005/http://www.nytimes.com/2008/04/14/science/14wheeler.html |archive-date=22 November 2016}}</ref>
However the term was used by others around that time. Science writer Marcia Bartusiak traces the term "black hole" to physicist [[Robert H. Dicke]], who in the early 1960s reportedly compared the phenomenon to the [[Black Hole of Calcutta]], notorious as a prison where people entered but never left alive.
The term "black hole" was used in print by ''[[Life (magazine)|Life]]'' and ''[[Science News]]'' magazines in 1963, and by science journalist Ann Ewing in her article {{" '}}Black Holes' in Space", dated 18 January 1964, which was a report on a meeting of the [[American Association for the Advancement of Science]] held in Cleveland, Ohio.<ref name=Bartusiak>{{Cite book |last=Bartusiak |first=Marcia |title=Black Hole: How an Idea Abandoned by Newtonians, Hated by Einstein, and Gambled On by Hawking Became Loved |date=2015 |publisher=Yale University Press |isbn=978-0-300-21363-8 |location=New Haven, CT}}</ref>

== Properties and structure ==
The [[escape velocity]] from a black hole exceeds the [[speed of light]]. The formula for escape velocity is 
<math display="block"> V = \sqrt{2MG/R}</math> 
for an object at radius {{mvar|R}} from a spherical mass {{mvar|M}}, with {{mvar|G}} being the gravitational constant. When the velocity is the speed of light, {{mvar|c}}, the radius, <math>R_s = 2MG/c^2,</math> is called the [[Schwarzschild radius]].<ref>{{Cite book |last=Susskind |first=Leonard |author-link=Leonard Susskind |title=The black hole war: my battle with Stephen Hawking to make the world safe for quantum mechanics |title-link=The Black Hole War |date=2008 |publisher=Little, Brown |isbn=978-0-316-01640-7 |edition=1st |location=New York |oclc=181603165}}</ref>{{rp|27}}
A technical definition of a black hole is any object whose mass is contained in a radius smaller than its [[Schwarzschild radius]], a limit derived from one solution to the equations of general relativity.<ref>{{Cite book |last=Zee |first=Anthony |title=Einstein Gravity in a Nutshell |date=2013 |publisher=Princeton University Press |isbn=978-0-691-14558-7 |edition=1st |series=In a Nutshell Series |location=Princeton}}</ref>{{rp|410}}

The [[no-hair theorem]] postulates that, once it achieves a stable condition after formation, a black hole has only three independent physical properties: mass, electric charge, and angular momentum; the black hole is otherwise featureless. If the conjecture is true, any two black holes that share the same values for these properties, or parameters, are indistinguishable from one another. The degree to which the conjecture is true for real black holes under the laws of modern physics is currently an unsolved problem.<ref name="HeuslerNoHair">{{Cite journal |last=Heusler |first=M. |date=2012 |title=Stationary Black Holes: Uniqueness and Beyond |journal=Living Reviews in Relativity |volume=15 |issue=7 |article-number=7|doi=10.12942/lrr-2012-7 |doi-access=free |pmid=28179837 |pmc=5255892 |arxiv=1205.6112 |bibcode=2012LRR....15....7C}}</ref>

These properties are special because they are visible from outside a black hole. For example, a charged black hole repels other like charges just like any other charged object. Similarly, the total mass inside a sphere containing a black hole can be found by using the gravitational analogue of [[Gauss's law]] (through the [[ADM mass]]), far away from the black hole.<ref>{{harvnb|Carroll|2004|p=253}}</ref> Likewise, the angular momentum (or spin) can be measured from far away using [[frame dragging]] by the [[gravitomagnetism|gravitomagnetic field]], through for example the [[Lense–Thirring precession|Lense–Thirring effect]].<ref>{{Cite journal|last=Reynolds|first=Christopher S.|date=January 2019|title=Observing black holes spin|url=https://www.nature.com/articles/s41550-018-0665-z|journal=Nature Astronomy|volume=3|issue=1|pages=41–47|doi=10.1038/s41550-018-0665-z|issn=2397-3366|arxiv=1903.11704|bibcode=2019NatAs...3...41R|s2cid=85543351|access-date=21 August 2020|archive-date=18 November 2020|archive-url=https://web.archive.org/web/20201118092121/https://www.nature.com/articles/s41550-018-0665-z|url-status=live}}</ref>

[[File:Anatomy of a Black Hole.jpg|center|thumb|450x450px|An artistic depiction of a black hole and its features]]
When an object falls into a black hole, any information about the shape of the object or distribution of charge on it is evenly distributed along the horizon of the black hole, and is lost to outside observers. The behaviour of the horizon in this situation is a [[dissipative system]] that is closely analogous to that of a conductive stretchy membrane with friction and [[electrical resistance]]—the [[membrane paradigm]].<ref>{{Cite book |title=Black holes: the membrane paradigm |last1=Thorne |first1=K. S. |author-link1=Kip Thorne |last2=Price |first2=R. H. |author-link2=Richard H. Price |publisher=Yale University Press |date=1986 |isbn=978-0-300-03770-8}}</ref> This is different from other [[field theory (physics)|field theories]] such as electromagnetism, which do not have any friction or resistivity at the microscopic level, because they are [[T-symmetry|time-reversible]].<ref name="math_ucr_edu">{{cite web |url=http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/info_loss.html |title=The Black Hole Information Loss Problem |website=Usenet Physics FAQ |last=Anderson |first=Warren G. |date=1996 |access-date=24 March 2009 |archive-url=https://web.archive.org/web/20090122223839/http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/info_loss.html |archive-date=22 January 2009}}</ref><ref name="Preskill1994">{{cite conference |last=Preskill |first=J. |author-link1=John Preskill |url=http://www.theory.caltech.edu/~preskill/talks/blackholes.pdf |title=Black holes and information: A crisis in quantum physics |date=21 October 1994 |conference=Caltech Theory Seminar |archive-url=https://web.archive.org/web/20080518054438/http://www.theory.caltech.edu/~preskill/talks/blackholes.pdf |archive-date=18 May 2008 |access-date=17 May 2009 }}</ref>

Because a black hole eventually achieves a stable state with only three parameters, there is no way to avoid losing information about the initial conditions: the gravitational and electric fields of a black hole give very little information about what went in. The information that is lost includes every quantity that cannot be measured far away from the black hole horizon, including [[Conservation law|approximately conserved]] [[quantum number]]s such as the total [[baryon number]] and [[lepton number]]. This behaviour is so puzzling that it has been called the [[black hole information loss paradox]].<ref name="math_ucr_edu" /><ref name="Preskill1994"/>

=== Physical properties ===
[[File:Black_Hole_Shadow.gif|thumb|350x350px|Radii for shadow and photon sphere relative to event horizon.]]
The simplest static black holes have mass but neither electric charge nor angular momentum. These black holes are often referred to as Schwarzschild black holes after [[Karl Schwarzschild]] who discovered this [[Solutions of the Einstein field equations|solution]] in 1916.<ref name="Schwarzschild1916" /> According to [[Birkhoff's theorem (relativity)|Birkhoff's theorem]], it is the only [[Vacuum solution (general relativity)|vacuum solution]] that is [[Spherically symmetric spacetime|spherically symmetric]].<ref>{{harvnb|Hawking|Ellis|1973|loc=Appendix B}}</ref> This means there is no observable difference at a distance between the gravitational field of such a black hole and that of any other spherical object of the same mass. The popular notion of a black hole "sucking in everything" in its surroundings is therefore correct only near a black hole's horizon; far away, the external gravitational field is identical to that of any other body of the same mass.<ref>{{Cite book |first1=Michael A. |last1=Seeds |first2=Dana E. |last2=Backman |title=Perspectives on Astronomy |page=167 |publisher=Cengage Learning |date=2007 |isbn=978-0-495-11352-2 |url=https://books.google.com/books?id=CXom04KGIL8C&pg=PA167|url-status=live |archive-url=https://web.archive.org/web/20160810211808/https://books.google.com/books?id=CXom04KGIL8C&pg=PA167 |archive-date=10 August 2016}}</ref>

Solutions describing more general black holes also exist. Non-rotating [[charged black hole]]s are described by the [[Reissner–Nordström metric]], while the Kerr metric describes a non-charged rotating black hole. The most general [[stationary spacetime|stationary]] black hole solution known is the Kerr–Newman metric, which describes a black hole with both charge and angular momentum.<ref name=shapiro_teukolsky1983>{{cite book |last1=Shapiro |first1=S. L. |last2=Teukolsky |first2=S. A. |author2-link=Saul Teukolsky |title=Black holes, white dwarfs, and neutron stars: the physics of compact objects |page=357 |publisher=John Wiley and Sons |date=1983 |isbn=978-0-471-87316-7}}</ref>

While the mass of a black hole can take any positive value, the charge and angular momentum are constrained by the mass. The total electric charge&nbsp;''Q'' and the total angular momentum&nbsp;''J'' are expected to satisfy the inequality
<math display="block">\frac{Q^2}{4\pi\epsilon_0} + \frac{c^2 J^2}{G M^2} \le G M^2</math>
for a black hole of mass ''M''. Black holes with the minimum possible mass satisfying this inequality are called [[extremal black hole|extremal]]. Solutions of Einstein's equations that violate this inequality exist, but they do not possess an event horizon. These solutions have so-called [[naked singularity|naked singularities]] that can be observed from the outside, and hence are deemed ''unphysical''. The [[cosmic censorship hypothesis]] rules out the formation of such singularities, when they are created through the gravitational collapse of [[energy conditions|realistic matter]].<ref name="wald 1997">{{cite book |last=Wald |first=R. M. |author-link=Robert Wald |title=Black Holes, Gravitational Radiation and the Universe |editor1=Iyer, B. R. |editor2=Bhawal, B. |chapter=Gravitational Collapse and Cosmic Censorship |arxiv=gr-qc/9710068 |date=1997 |pages=69–86 |location=Dordrecht |publisher=Springer |doi=10.1007/978-94-017-0934-7 |isbn=978-94-017-0934-7}}</ref> This is supported by numerical simulations.<ref>{{Cite journal |last=Berger |first=B. K.|author-link= Beverly Berger |date=2002 |title=Numerical Approaches to Spacetime Singularities |journal=Living Reviews in Relativity |volume=5 |issue=1 |pages=2002–1|article-number=1 |bibcode=2002LRR.....5....1B |doi=10.12942/lrr-2002-1 |doi-access=free |pmid=28179859 |pmc=5256073 |arxiv=gr-qc/0201056}}</ref>

Due to the relatively large strength of the [[electromagnetism|electromagnetic force]], black holes forming from the collapse of stars are expected to retain the nearly neutral charge of the star. Rotation, however, is expected to be a universal feature of compact astrophysical objects. The black-hole candidate binary X-ray source [[GRS 1915+105]]<ref>{{Cite journal |first1=J. E. |last1=McClintock |first2=R. |last2=Shafee |first3=R. |last3=Narayan |first4=R. A. |last4=Remillard |first5=S. W. |last5=Davis |first6=L.-X. |last6=Li |title=The Spin of the Near-Extreme Kerr Black Hole GRS 1915+105 |journal=Astrophysical Journal |volume=652 |issue=1 |date=2006 |pages=518–539 |arxiv=astro-ph/0606076 |doi=10.1086/508457|bibcode=2006ApJ...652..518M|s2cid=1762307 }}</ref> appears to have an angular momentum near the maximum allowed value. That uncharged limit is<ref name="50SMBH" />
<math display="block">J \le \frac{GM^{2}}{c},</math>
allowing definition of a [[dimensionless]] spin parameter such that<ref name="50SMBH" />
<math display="block"> 0 \le \frac{cJ}{GM^{2}}\le 1.</math><ref name="50SMBH">{{cite journal |doi=10.1103/PhysRevLett.118.221101 |pmid=28621973 |title=GW170104: Observation of a 50-Solar-Mass Binary Black Hole Coalescence at Redshift 0.2 |journal=[[Physical Review Letters]] |date=1 June 2017 |first=B. P. |last=Abbott |collaboration=[[LIGO Scientific Collaboration]] and Virgo Collaboration |volume=118 |issue=22 |article-number=221101 |arxiv=1706.01812 |bibcode=2017PhRvL.118v1101A|s2cid=206291714 }}</ref>{{refn|group=Note|The value of ''cJ/GM{{sup|2}}'' can exceed{{nbsp}}1 for objects other than black holes. The largest value known for a neutron star is ≤ 0.4, and commonly used equations of state would limit that value to < 0.7.<ref name="PRL-171016">{{cite journal |last1=Abbott |first1=B. P. |display-authors=et al |collaboration=[[LIGO Scientific Collaboration]] & [[Virgo interferometer|Virgo Collaboration]] |title=GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral |journal=Physical Review Letters |date=16 October 2017 |volume=119 |issue=16 |article-number=161101 |doi=10.1103/PhysRevLett.119.161101 |pmid=29099225 |arxiv=1710.05832 |bibcode=2017PhRvL.119p1101A|s2cid=217163611 }}</ref>}}

{|class="wikitable" style="float:right; margin:0 0 0.5em 1em;"
|+ Black hole classifications
|-
! Class !! Approx.<br />mass !! Approx.<br />radius
|-
|[[Supermassive black hole#Ultramassive black holes|Ultramassive black hole]] ||style="text-align: center;"| {{10^|9}}–{{solar mass|{{10^|11}}}}  ||style="text-align: center;"|>1,000 [[Astronomical unit|AU]]
|-
|[[Supermassive black hole]] ||style="text-align: center;"| {{10^|6}}–{{solar mass|{{10^|9}}}} ||style="text-align: center;"|0.001–400 [[Astronomical unit|AU]]
|-
|[[Intermediate-mass black hole]] ||style="text-align: center;"| {{10^|2}}–{{solar mass|{{10^|5}}}} ||style="text-align: center;"|10{{sup|3}} km ≈ [[Earth radius|''R''{{sub|Earth}}]]
|-
|[[Stellar black hole]] ||style="text-align: center;"| {{solar mass|2–150}} ||style="text-align: center;"|30&nbsp;km
|-
|[[Micro black hole]] ||style="text-align: center;"|up to ''M''{{sub|[[Moon]]}} ||style="text-align: center;"|up to 0.1&nbsp;mm
|}
Black holes are commonly classified according to their mass, independent of angular momentum, ''J''. The size of a black hole, as determined by the radius of the event horizon, or Schwarzschild radius, is proportional to the mass, ''M'', through
<math display="block">r_\mathrm{s}=\frac{2GM}{c^2} \approx 2.95\, \frac{M}{M_\odot}~\mathrm{km,}</math>
where ''r''{{sub|s}} is the Schwarzschild radius and {{solar mass}} is the [[solar mass|mass of the Sun]].<ref>{{harvnb|Wald|1984|pp=124–125}}</ref> For a black hole with nonzero spin or electric charge, the radius is smaller,{{refn|group=Note|The (outer) event horizon radius scales as: <math>M + \sqrt{M^2 - {{(J/M)}}^2 - Q^2}.</math>}} until an extremal black hole could have an event horizon close to<ref>{{cite journal |last1=Saa |first1=Alberto |last2=Santarelli |first2=Raphael |title=Destroying a near-extremal Kerr–Newman black hole |journal=Physical Review D |date=18 July 2011 |volume=84 |issue=2 |page=027501 |doi=10.1103/PhysRevD.84.027501 |arxiv=1105.3950 |bibcode=2011PhRvD..84b7501S|s2cid=118487989 }}</ref>
<math display="block">r_\mathrm{+}=\frac{GM}{c^2}.</math>

=== Event horizon ===
{{Main|Event horizon}}
{{multiple image
| align             = right
| direction         = vertical
| width             = 300
| image1            = BH-no-escape-1.svg
| caption1          = Far away from the black hole, a particle can move in any direction, as illustrated by the set of arrows. It is restricted only by the speed of light.
| image2            = BH-no-escape-2.svg
| caption2          = Closer to the black hole, spacetime starts to deform. There are more paths going towards the black hole than paths moving away.{{refn|The set of possible paths, or more accurately the future [[light cone]] containing all possible [[world line]]s (in this diagram the light cone is represented by the V-shaped region bounded by arrows representing light ray world lines), is tilted in this way in [[Eddington–Finkelstein coordinates]] (the diagram is a "cartoon" version of an Eddington–Finkelstein coordinate diagram), but in other coordinates the light cones are not tilted in this way, for example in [[Schwarzschild coordinates]] they narrow without tilting as one approaches the event horizon, and in [[Kruskal–Szekeres coordinates]] the light cones do not change shape or orientation at all.<ref>{{harvnb|Misner|Thorne|Wheeler|1973|p=848}}</ref>|group="Note"}}
| image3            = BH-no-escape-3.svg
| caption3          = Inside of the event horizon, all paths bring the particle closer to the centre of the black hole. It is no longer possible for the particle to escape.
}}

The defining feature of a black hole is the appearance of an event horizon, a boundary in [[spacetime]] through which matter and light can pass only inward towards the mass of the black hole. Nothing, not even light, can escape from inside the event horizon.<ref>{{cite book |title=The New Physics |edition=illustrated |first1=Paul |last1=Davies |publisher=Cambridge University Press |year=1992 |isbn=978-0-521-43831-5 |page=26 |url=https://books.google.com/books?id=akb2FpZSGnMC |access-date=25 September 2020 |archive-date=17 August 2021 |archive-url=https://web.archive.org/web/20210817161727/https://books.google.com/books?id=akb2FpZSGnMC |url-status=live }} [https://books.google.com/books?id=akb2FpZSGnMC&pg=PA26 Extract of page 26] {{Webarchive|url=https://web.archive.org/web/20210815222341/https://books.google.com/books?id=akb2FpZSGnMC&pg=PA26 |date=15 August 2021 }}</ref><ref>{{cite book |title=A Student's Guide to the Mathematics of Astronomy |edition=illustrated |first1=Daniel |last1=Fleisch |first2=Julia |last2=Kregenow |publisher=Cambridge University Press |year=2013 |isbn=978-1-107-03494-5 |page=168 |url=https://books.google.com/books?id=x4gaBQAAQBAJ |access-date=25 September 2020 |archive-date=17 August 2021 |archive-url=https://web.archive.org/web/20210817045139/https://books.google.com/books?id=x4gaBQAAQBAJ |url-status=live }} [https://books.google.com/books?id=x4gaBQAAQBAJ&pg=PA168 Extract of page 168] {{Webarchive|url=https://web.archive.org/web/20210817113029/https://books.google.be/books?id=x4gaBQAAQBAJ&pg=PA168 |date=17 August 2021 }}</ref> The event horizon is referred to as such because if an event occurs within the boundary, information from that event cannot reach an outside observer, making it impossible to determine whether such an event occurred.<ref>{{harvnb|Wheeler|2007|p=179}}</ref>

As predicted by general relativity, the presence of a mass deforms spacetime in such a way that the paths taken by particles bend towards the mass.<ref>{{harvnb|Carroll|2004|loc=Ch. 5.4 and 7.3}}</ref> At the event horizon of a black hole, this deformation becomes so strong that there are no paths that<!--to avoid false positives in search for 'that led/lead' typo--> lead away from the black hole.<ref>{{cite web |title=Singularities and Black Holes > Lightcones and Causal Structure |url=https://plato.stanford.edu/entries/spacetime-singularities/lightcone.html |website=plato.stanford.edu |publisher=[[Stanford Encyclopedia of Philosophy]] |access-date=11 March 2018 |archive-date=17 May 2019 |archive-url=https://web.archive.org/web/20190517122738/https://plato.stanford.edu/entries/spacetime-singularities/lightcone.html |url-status=live }}</ref>

In a thought experiment, a distant observer can imagine clocks near a black hole which would appear to tick more slowly than those farther away from the black hole.<ref>{{harvnb|Carroll|2004|p=217}}</ref> This effect, known as [[gravitational time dilation]], would also cause an object falling into a black hole to appear to slow as it approaches the event horizon, taking an infinite amount of time to reach it.<ref>{{harvnb|Carroll|2004|p=218}}</ref> All processes on this object would appear to slow down, from the viewpoint of a fixed outside observer, and any light emitted by the object to appear redder and dimmer, an effect known as [[gravitational redshift]].<ref>{{cite web |url=http://nrumiano.free.fr/Estars/int_bh.html |title=Inside a black hole |website=Knowing the universe and its secrets |access-date=26 March 2009 |archive-url=https://web.archive.org/web/20090423053437/http://nrumiano.free.fr/Estars/int_bh.html |archive-date=23 April 2009 }}</ref> Eventually, the falling object fades away until it can no longer be seen. Typically this process happens very rapidly with an object disappearing from view within less than a second.<ref>{{cite web |title=What happens to you if you fall into a black hole |url=http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/fall_in.html |website=math.ucr.edu |publisher=[[John Baez]] |access-date=11 March 2018 |archive-date=13 February 2019 |archive-url=https://web.archive.org/web/20190213124648/http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/fall_in.html |url-status=live }}</ref>

On the other hand, imaginary, indestructible observers falling into a black hole would not notice any of these effects as they cross the event horizon. Their own clocks appear to them to tick normally, they cross the event horizon after a finite time without noting any singular behaviour.
In [[general relativity]], it is impossible to determine the location of the event horizon from local observations, due to Einstein's [[equivalence principle]].<ref>{{harvnb|Carroll|2004|p=222}}</ref><ref>{{cite news |title=Watch: Three Ways an Astronaut Could Fall Into a Black Hole |url=https://news.nationalgeographic.com/news/2014/01/140130-black-holes-stephen-hawking-work-space-astronomy/ |access-date=13 March 2018 |date=1 February 2014 |archive-date=15 April 2019 |archive-url=https://web.archive.org/web/20190415101947/https://news.nationalgeographic.com/news/2014/01/140130-black-holes-stephen-hawking-work-space-astronomy/ }}</ref>

The [[topology]] of the event horizon of a black hole at equilibrium is always spherical.{{refn|This is true only for four-dimensional spacetimes. In higher dimensions more complicated horizon topologies like a [[Higher-dimensional Einstein gravity#Black hole uniqueness|black ring]] are possible.<ref>{{cite journal |first1=R. |last1=Emparan |first2=H. S. |last2=Reall |title=Black Holes in Higher Dimensions |journal=Living Reviews in Relativity |volume=11 |issue=6 |page=6 |date=2008 |arxiv=0801.3471 |bibcode=2008LRR....11....6E |doi=10.12942/lrr-2008-6 |doi-access=free |pmid=28163607 |pmc=5253845}}</ref><ref>{{Cite book |last1=Obers |first1=N. A. |title=Physics of Black Holes |editor1-last=Papantonopoulos |editor1-first=Eleftherios |volume=769 |pages=211–258 |date=2009 |doi=10.1007/978-3-540-88460-6 |arxiv=0802.0519 |series=Lecture Notes in Physics |location=Berlin |publisher=Springer |isbn=978-3-540-88459-0 |bibcode=2009LNP...769.....P |url=https://cds.cern.ch/record/1164174/files/978-3-540-88460-6_BookTOC.pdf |access-date=27 July 2018 |archive-date=26 July 2018 |archive-url=https://web.archive.org/web/20180726103141/https://cds.cern.ch/record/1164174/files/978-3-540-88460-6_BookTOC.pdf |url-status=live }}</ref>|group="Note"}}<ref>{{harvnb|Hawking|Ellis|1973|loc=Ch. 9.3}}</ref> For non-rotating (static) black holes the geometry of the event horizon is precisely spherical, while for rotating black holes the event horizon is oblate.<ref name= "Smarr1973">{{cite journal|last1= Smarr|first1= L.|title= Surface Geometry of Charged Rotating Black Holes |journal= Physical Review D|volume= 7|issue= 2|year= 1973|pages= 289–295|doi= 10.1103/PhysRevD.7.289|bibcode= 1973PhRvD...7..289S}}</ref><ref name= "Wiltshire2009">{{cite book|author= Visser, M.|editor1= Wiltshire, D.L.|editor2= Visser, M.|editor3= Scott, S.M.|title= The Kerr Spacetime: Rotating Black Holes in General Relativity|url= https://books.google.com/books?id=wymJBq_80Q0C|chapter= The Kerr spacetime: A brief introduction|date= 22 January 2009|publisher= Cambridge University Press|isbn= 978-0-521-88512-6|arxiv= 0706.0622|access-date= 12 January 2020|archive-date= 20 May 2020|archive-url= https://web.archive.org/web/20200520134643/https://books.google.com/books?id=wymJBq_80Q0C|url-status= live}}</ref><ref name= "Delgado2018">{{cite journal|last1= Delgado|first1= J.F. M.|last2= Herdeiro|first2= C.A. R.|last3= Radu|first3= E.|title= Horizon geometry for Kerr black holes with synchronized hair|journal= Physical Review D|volume= 97|issue= 12|page= 124012|year= 2018|doi= 10.1103/PhysRevD.97.124012|bibcode= 2018PhRvD..97l4012D|hdl= 10773/24121|arxiv= 1804.04910|s2cid= 55732213}}</ref>

=== Singularity ===
{{Main|Gravitational singularity}}

At the centre of the unrealistically simple Schwarzschild model of a black hole is a [[gravitational singularity]], a region where the spacetime curvature becomes infinite.<ref name="Carroll 2004 205">{{harvnb|Carroll|2004|p=205}}</ref> For a non-rotating black hole, this region takes the shape of a single point; for a rotating black hole it is smeared out to form a [[ring singularity]] that lies in the plane of rotation.<ref>{{harvnb|Carroll|2004|pp=264–265}}</ref> In both cases, the singular region has zero volume. It can also be shown that the singular region contains all the mass of the black hole solution.<ref>{{harvnb|Carroll|2004|p=252}}</ref> The singular region can thus be thought of as having infinite [[mass density|density]].<ref>{{cite news |title=Sizes of Black Holes? How Big is a Black Hole? |url=https://www.skyandtelescope.com/astronomy-resources/how-big-is-a-black-hole/ |access-date=9 October 2018 |work=[[Sky & Telescope]] |date=22 July 2014 |archive-date=3 April 2019 |archive-url=https://web.archive.org/web/20190403035741/https://www.skyandtelescope.com/astronomy-resources/how-big-is-a-black-hole/ |url-status=live }}</ref>

Even though the Schwarzschild model is not valid at the singularity,<ref name="Carroll 2004 205"/> observers falling into a Schwarzschild black hole (i.e., non-rotating and not charged) cannot avoid being carried into the singularity once they cross the event horizon. They can prolong the experience by accelerating away to slow their descent, but only up to a limit.<ref>{{Cite journal |last1=Lewis |first1=G. F. |last2=Kwan |first2=J. |title=No Way Back: Maximizing Survival Time Below the Schwarzschild Event Horizon |journal=Publications of the Astronomical Society of Australia |volume=24 |issue=2 |pages=46–52 |date=2007 |doi=10.1071/AS07012 |arxiv=0705.1029 |bibcode=2007PASA...24...46L |s2cid=17261076}}</ref> When they reach the singularity, they are crushed to infinite density and their mass is added to the total of the black hole. Before that happens, they will have been torn apart by the growing [[tidal force]]s in a process sometimes referred to as [[spaghettification]] or the "noodle effect".<ref>{{harvnb|Wheeler|2007|p=182}}</ref> <!-- possibly add something related to Mixmaster/BKL dynamics here? -->

In the case of a charged (Reissner–Nordström) or rotating (Kerr) black hole, it is possible to avoid the singularity. Extending these solutions as far as possible reveals the hypothetical possibility of exiting the black hole into a different spacetime with the black hole acting as a [[wormhole]].<ref>{{harvnb|Carroll|2004|pp=257–259 and 265–266}}</ref> The possibility of travelling to another universe is, however, only theoretical since any perturbation would destroy this possibility.<ref>{{Cite journal |title=Black holes: the inside story |first1=S. |last1=Droz |first2=W. |last2=Israel |first3=S. M. |last3=Morsink |journal=Physics World |volume=9 |issue=1 |pages=34–37 |date=1996|bibcode=1996PhyW....9...34D |doi=10.1088/2058-7058/9/1/26}}</ref> It also appears to be possible to follow [[closed timelike curve]]s (returning to one's own past) around the Kerr singularity, which leads to problems with [[causality (physics)|causality]] like the [[grandfather paradox]].<ref>{{harvnb|Carroll|2004|p=266}}</ref> It is expected that none of these peculiar effects would survive in a proper quantum treatment of rotating and charged black holes.<ref>{{cite journal |last1=Poisson |first1=E. |last2=Israel |first2=W. |title=Internal structure of black holes |journal=Physical Review D |volume=41 |issue=6 |pages=1796–1809 |date=1990 |doi=10.1103/PhysRevD.41.1796 |pmid=10012548 |bibcode=1990PhRvD..41.1796P}}</ref>

The appearance of singularities in general relativity signals the breakdown of the theory.<ref>{{harvnb|Wald|1984|p=212}}</ref> This breakdown occurs where [[quantum effects]] should describe these actions, due to the extremely high density and therefore particle interactions. To date, it has not been possible to combine quantum and gravitational effects into a single theory, although there exist attempts to formulate such a theory of [[quantum gravity]]. It is generally expected that such a theory will not feature singularities.<ref>{{cite web |url=http://www.damtp.cam.ac.uk/user/gr/public/bh_hawk.html |title=Black Holes and Quantum Gravity |website=Cambridge Relativity and Cosmology |last=Hamade |first=R. |date=1996 |publisher=University of Cambridge |access-date=26 March 2009 |archive-url=https://web.archive.org/web/20090407043337/http://www.damtp.cam.ac.uk/user/gr/public/bh_hawk.html |archive-date=7 April 2009 }}</ref><ref>{{cite web |url=http://imagine.gsfc.nasa.gov/docs/ask_astro/answers/980420b.html |title=Ask an Astrophysicist: Quantum Gravity and Black Holes |last=Palmer |first=D. |publisher=NASA |access-date=26 March 2009 |archive-url=https://web.archive.org/web/20090328064842/http://imagine.gsfc.nasa.gov/docs/ask_astro/answers/980420b.html |archive-date=28 March 2009 }}</ref>

=== Photon sphere ===
{{Main|Photon sphere}}
[[File:4 trajectoires d'un photon autour d'un trou noir.png |thumb |Orbits of four photons around a [[Schwarzschild metric|Schwarzschild black hole]].]]
The [[photon sphere]] is a spherical boundary where photons that move on tangents to that sphere would be trapped in a non-stable but circular orbit around the black hole.<ref name="Cramer 1997">{{Cite journal |last=Cramer |first=Claes R. |date=1997 |title=Using the Uncharged Kerr Black Hole as a Gravitational Mirror |journal=General Relativity and Gravitation |volume=29 |issue=4 |pages=445–454 |doi=10.1023/A:1018878515046 |arxiv=gr-qc/9510053 |bibcode=1997GReGr..29..445C |s2cid=9517046}}</ref>
For non-rotating black holes, the photon sphere has a radius 1.5 times the Schwarzschild radius. Their orbits would be [[instability|dynamically unstable]], hence any small perturbation, such as a particle of infalling matter, would cause an instability that would grow over time, either setting the photon on an outward trajectory causing it to escape the black hole, or on an inward spiral where it would eventually cross the event horizon.<ref name=prd84_6>{{Cite journal |last1=Nitta |first1=Daisuke |last2=Chiba |first2=Takeshi |last3=Sugiyama |first3=Naoshi |title=Shadows of colliding black holes |journal=Physical Review D |volume=84 |issue=6 |page=063008 |date=September 2011 |doi=10.1103/PhysRevD.84.063008 |bibcode=2011PhRvD..84f3008N |arxiv=1106.2425 |s2cid=119264596}}</ref>

While light can still escape from the photon sphere, any light that crosses the photon sphere on an inbound trajectory will be captured by the black hole. Hence any light that reaches an outside observer from the photon sphere must have been emitted by objects between the photon sphere and the event horizon.<ref name=prd84_6 /> For a Kerr black hole the radius of the photon sphere depends on the spin parameter and on the details of the photon orbit, which can be prograde (the photon rotates in the same sense of the black hole spin) or retrograde.<ref name="Bardeen1972">{{Cite journal|last1=Bardeen|first1=James M.|last2=Press|first2=William H.|last3=Teukolsky|first3=Saul A.|date=1 December 1972|title=Rotating Black Holes: Locally Nonrotating Frames, Energy Extraction, and Scalar Synchrotron Radiation|journal=The Astrophysical Journal|volume=178|pages=347–370|doi=10.1086/151796|bibcode=1972ApJ...178..347B}}</ref><ref>{{Cite web|title=Black Hole Calculator|url=https://www.fabiopacucci.com/resources/black-hole-calculator/|access-date=29 September 2020|website=Fabio Pacucci|archive-date=21 October 2020|archive-url=https://web.archive.org/web/20201021154805/https://www.fabiopacucci.com/resources/black-hole-calculator/|url-status=live}}</ref>

=== Ergosphere ===
{{Main|Ergosphere}}
[[File:Ergosphere and event horizon of a rotating black hole (no animation).gif|thumb|The ergosphere is a region outside of the event horizon, where objects cannot remain in place.<ref name=viss>{{cite arXiv |eprint=0706.0622 |last1=Visser |first1=Matt |title=The Kerr spacetime: A brief introduction |class=gr-qc |year=2007 |at=page 35, Fig. 3}}</ref>]]

Rotating black holes are surrounded by a region of spacetime in which it is impossible to stand still, called the ergosphere. This is the result of a process known as [[frame-dragging]]; general relativity predicts that any rotating mass will tend to slightly "drag" along the spacetime immediately surrounding it. Any object near the rotating mass will tend to start moving in the direction of rotation. For a rotating black hole, this effect is so strong near the event horizon that an object would have to move faster than the [[speed of light]] in the opposite direction to just stand still.<ref>{{harvnb|Carroll|2004|loc=Ch. 6.6}}</ref>

The ergosphere of a black hole is a volume bounded by the black hole's event horizon and the ''ergosurface'', which coincides with the event horizon at the poles but is at a much greater distance around the equator.<ref name=viss />

Objects and radiation can escape normally from the ergosphere. Through the [[Penrose process]], objects can emerge from the ergosphere with more energy than they entered with. The extra energy is taken from the rotational energy of the black hole. Thereby the rotation of the black hole slows down.<ref>{{harvnb|Carroll|2004|loc=Ch. 6.7}}</ref> A variation of the Penrose process in the presence of strong magnetic fields, the [[Blandford–Znajek process]] is considered a likely mechanism for the enormous luminosity and relativistic jets of [[quasars]] and other [[active galactic nuclei]].

=== Innermost stable circular orbit (ISCO) ===
{{Main|Innermost stable circular orbit}}

In [[Newton's law of universal gravitation|Newtonian gravity]], [[test particle]]s can stably orbit at arbitrary distances from a central object. In general relativity, however, there exists an innermost stable circular orbit (often called the ISCO), for which any infinitesimal inward perturbations to a circular orbit will lead to spiraling into the black hole, and any outward perturbations will, depending on the energy, result in spiraling in, stably orbiting between apastron and periastron, or escaping to infinity.<ref>{{harvnb|Misner|Thorne|Wheeler|1973|loc=Box 25.6}}</ref> The location of the ISCO depends on the spin of the black hole, in the case of a Schwarzschild black hole (spin zero) is:
<math display="block">r_{\rm ISCO}=3 \, r_s=\frac{6 \, GM}{c^2}, </math>
and decreases with increasing black hole spin for particles orbiting in the same direction as the spin.<ref name="Bardeen1972"/>

=== Plunging region ===
The final observable region of spacetime around a black hole is called the plunging region. In this area it is no longer possible for matter to follow circular orbits or to stop a final descent into the black hole. Instead it will rapidly plunge toward the black hole close to the speed of light.<ref>{{cite web |title=First proof of black hole 'plunging regions' |url=https://www.physics.ox.ac.uk/news/first-proof-black-hole-plunging-regions |department=Department of Physics |publisher=[[University of Oxford]] |date=16 May 2024}}</ref><ref>{{cite journal |last1=Mummery |first1=Andrew |last2=Ingram |first2=Adam |last3=Davis |first3=Shane |last4=Fabian |first4=Andrew |title=Continuum emission from within the plunging region of black hole discs |journal=Monthly Notices of the Royal Astronomical Society |volume=531 |issue=1 |pages=366–386 |date=June 2024 |doi=10.1093/mnras/stae1160|doi-access=free |arxiv=2405.09175 }}</ref>

== Formation and evolution ==
Given the bizarre character of black holes, it was long questioned whether such objects could actually exist in nature or whether they were merely pathological solutions to Einstein's equations. Einstein himself wrongly thought black holes would not form, because he held that the angular momentum of collapsing particles would stabilise their motion at some radius.<ref>{{Cite journal |last=Einstein |first=A. |title=On A Stationary System With Spherical Symmetry Consisting of Many Gravitating Masses |journal=Annals of Mathematics |volume=40 |issue=4 |pages=922–936 |date=1939 |doi=10.2307/1968902 |bibcode=1939AnMat..40..922E|jstor=1968902|s2cid=55495712 |url=http://pdfs.semanticscholar.org/8dd0/dfafef0c53c428fdc3b58f8099aafcf7d089.pdf |archive-url=https://web.archive.org/web/20190228153449/http://pdfs.semanticscholar.org/8dd0/dfafef0c53c428fdc3b58f8099aafcf7d089.pdf |archive-date=28 February 2019 }}</ref> This led the general relativity community to dismiss all results to the contrary for many years. However, a minority of relativists continued to contend that black holes were physical objects,<ref>{{cite book |chapter=The Kerr and Kerr-Schild metrics |first=R. P. |last=Kerr |title=The Kerr Spacetime |editor1-first=D. L. |editor1-last=Wiltshire |editor2-first=M. |editor2-last=Visser |editor3-first=S. M. |editor3-last=Scott |publisher=Cambridge University Press |date=2009 |isbn=978-0-521-88512-6 |arxiv=0706.1109 |bibcode=2007arXiv0706.1109K}}</ref> and by the end of the 1960s, they had persuaded the majority of researchers in the field that there is no obstacle to the formation of an event horizon.<ref>{{Cite web |last=Findley |first=Kate |date=27 December 2019 |title=The Discovery of Black Holes: From Theory to Actuality |url=https://www.wondriumdaily.com/the-discovery-of-black-holes-from-theory-to-actuality/ |archive-url=https://web.archive.org/web/20220925103539/https://www.wondriumdaily.com/the-discovery-of-black-holes-from-theory-to-actuality/ |archive-date=25 September 2022 |access-date=29 June 2022 |website=Wondrium Daily |language=en-US }}</ref>

Penrose demonstrated that once an event horizon forms, general relativity without quantum mechanics requires that a singularity will form within.<ref name=penrose1965 /> Shortly afterwards, Hawking showed that many cosmological solutions that describe the [[Big Bang]] have singularities without [[scalar field]]s or other [[exotic matter]].{{clarify|date=February 2016}} The [[Kerr solution]], the no-hair theorem, and the laws of black hole thermodynamics showed that the physical properties of black holes were simple and comprehensible, making them respectable subjects for research.<ref name=HawkingPenrose1970>{{Cite journal |first1=S. W. |last1=Hawking |author-link1=Stephen Hawking |first2=R. |last2=Penrose |author-link2=Roger Penrose |title=The Singularities of Gravitational Collapse and Cosmology |journal=[[Proceedings of the Royal Society A]] |volume=314 |issue=1519 |pages=529–548 |date=January 1970 |doi=10.1098/rspa.1970.0021|jstor=2416467 |bibcode=1970RSPSA.314..529H|doi-access=free}}</ref> Conventional black holes are formed by [[gravitational collapse]] of heavy objects such as stars, but they can also in theory be formed by other processes.<ref name="pacucci2016" /><ref name="carr primordial" />

=== Gravitational collapse ===
{{Main|Gravitational collapse}}
[[File:Images of gas cloud being ripped apart by the black hole at the centre of the Milky Way ESO.jpg|thumb|Gas cloud being ripped apart by black hole at the centre of the Milky Way (observations from 2006, 2010 and 2013 are shown in blue, green and red, respectively).<ref>{{cite news |title=Ripped Apart by a Black Hole |url=http://www.eso.org/public/news/eso1332/ |access-date=19 July 2013 |newspaper=ESO Press Release |archive-url=https://web.archive.org/web/20130721014626/http://www.eso.org/public/news/eso1332/ |archive-date=21 July 2013 }}</ref>]]

Gravitational collapse occurs when an object's internal [[pressure]] is insufficient to resist the object's own gravity. For stars this usually occurs either because a star has too little "fuel" left to maintain its temperature through [[stellar nucleosynthesis]], or because a star that would have been stable receives extra matter in a way that does not raise its core temperature. In either case the star's temperature is no longer high enough to prevent it from collapsing under its own weight.<ref name="Carroll5.8">{{harvnb|Carroll|2004|loc=Section 5.8}}</ref>

The collapse may be stopped by the [[Degenerate matter|degeneracy pressure]] of the star's constituents, allowing the condensation of matter into an exotic [[Degenerate matter|denser state]]. The result is one of the various types of [[compact star]]. Which type forms depends on the mass of the remnant of the original star left if the outer layers have been blown away (for example, in a [[Type II supernova]]). The mass of the remnant, the collapsed object that survives the explosion, can be substantially less than that of the original star. Remnants exceeding {{Solar mass|5}} are produced by stars that were over {{Solar mass|20}} before the collapse.<ref name="Carroll5.8" />

If the mass of the remnant exceeds about {{Solar mass|3–4}} (the Tolman–Oppenheimer–Volkoff limit<ref name="OV1939" />), either because the original star was very heavy or because the remnant collected additional mass through accretion of matter, even the degeneracy pressure of [[neutron]]s is insufficient to stop the collapse. No known mechanism (except possibly quark degeneracy pressure) is powerful enough to stop the implosion and the object will inevitably collapse to form a black hole.<ref name="Carroll5.8" />

The gravitational collapse of heavy stars is assumed to be responsible for the formation of [[stellar mass black hole]]s. [[Star formation]] in the early universe may have resulted in very massive stars, which upon their collapse would have produced black holes of up to {{Solar mass|{{10^|3}}}}. These black holes could be the seeds of the supermassive black holes found in the centres of most galaxies.<ref name="ReesVolonteri">{{Cite conference |first1=M. J. |series=Proceedings of the International Astronomical Union |last1=Rees |first2=M. |last2=Volonteri |author2-link=Marta Volonteri|title=Massive black holes: Formation and evolution |editor1-first=V. |editor1-last=Karas |editor2-first=G. |editor2-last=Matt |book-title=Black Holes from Stars to Galaxies – Across the Range of Masses |pages=51–58 |date=2007 |isbn=978-0-521-86347-6 |arxiv=astro-ph/0701512 |bibcode=2007IAUS..238...51R |doi=10.1017/S1743921307004681 |doi-access=free |s2cid=14844338 }}</ref> It has further been suggested that massive black holes with typical masses of ~{{Solar mass|{{10^|5}}}} could have formed from the direct collapse of gas clouds in the young universe.<ref name="pacucci2016">{{cite journal |last1=Pacucci |first1=F. |last2=Ferrara |first2=A. |last3=Grazian |first3=A. |last4=Fiore |first4=F. |last5=Giallongo |first5=E. |title=First Identification of Direct Collapse Black Hole Candidates in the Early Universe in CANDELS/GOODS-S |journal=Mon. Not. R. Astron. Soc. |volume=459 |issue=2 |year=2016 |page=1432 |doi=10.1093/mnras/stw725 |doi-access=free |arxiv=1603.08522 |bibcode=2016MNRAS.459.1432P|s2cid=118578313 }}</ref> These massive objects have been proposed as the seeds that eventually formed the earliest quasars observed already at redshift <math>z \sim 7</math>.<ref>{{Cite journal|last1=Bañados|first1=Eduardo|last2=Venemans|first2=Bram P.|last3=Mazzucchelli|first3=Chiara|last4=Farina|first4=Emanuele P.|last5=Walter|first5=Fabian|last6=Wang|first6=Feige|last7=Decarli|first7=Roberto|last8=Stern|first8=Daniel|last9=Fan|first9=Xiaohui|last10=Davies|first10=Frederick B.|last11=Hennawi|first11=Joseph F.|date=1 January 2018|title=An 800-million-solar-mass black hole in a significantly neutral Universe at a redshift of 7.5|journal=Nature|volume=553|issue=7689|pages=473–476|doi=10.1038/nature25180|pmid=29211709|arxiv=1712.01860|bibcode=2018Natur.553..473B|s2cid=205263326}}</ref> Some candidates for such objects have been found in observations of the young universe.<ref name="pacucci2016" />

While most of the energy released during gravitational collapse is emitted very quickly, an outside observer does not actually see the end of this process. Even though the collapse takes a finite amount of time from the [[frame of reference|reference frame]] of infalling matter, a distant observer would see the infalling material slow and halt just above the event horizon, due to gravitational time dilation. Light from the collapsing material takes longer and longer to reach the observer, with the light emitted just before the event horizon forms delayed an infinite amount of time. Thus the external observer never sees the formation of the event horizon; instead, the collapsing material seems to become dimmer and increasingly red-shifted, eventually fading away.<ref>{{cite journal |last1=Penrose |first1=R. |author-link1=Roger Penrose |title=Gravitational Collapse: The Role of General Relativity |journal=General Relativity and Gravitation |volume=34 |issue=7 |page=1141 |date=2002 |doi=10.1023/A:1016578408204 |url=http://www.imamu.edu.sa/Scientific_selections/abstracts/Physics/Gravitational%20Collapse%20The%20Role%20of%20General.pdf |bibcode=2002GReGr..34.1141P |s2cid=117459073|archive-url=https://web.archive.org/web/20130526224126/http://www.imamu.edu.sa/Scientific_selections/abstracts/Physics/Gravitational%20Collapse%20The%20Role%20of%20General.pdf |archive-date=26 May 2013 }}</ref>

==== Primordial black holes and the Big Bang ====
Gravitational collapse requires great density. In the current epoch of the universe these high densities are found only in stars, but in the early universe shortly after the Big Bang densities were much greater, possibly allowing for the creation of black holes. High density alone is not enough to allow black hole formation since a uniform mass distribution will not allow the mass to bunch up. In order for [[primordial black holes]] to have formed in such a dense medium, there must have been initial density perturbations that could then grow under their own gravity. Different models for the early universe vary widely in their predictions of the scale of these fluctuations. Various models predict the creation of primordial black holes ranging in size from a [[Planck mass]] (<math> m_P = \sqrt{\hbar c/G} </math> ≈ {{val|1.2|e=19|ul=GeV/c2}} ≈ {{val|2.2|e=-8|u=kg}}) to hundreds of thousands of solar masses.<ref name="carr primordial">{{cite book |last1=Carr |first1=B. J. |chapter=Primordial Black Holes: Do They Exist and Are They Useful? |editor1-first=H. |editor1-last=Suzuki |editor2-first=J. |editor2-last=Yokoyama |editor3-first=Y. |editor3-last=Suto |editor4-first=K. |editor4-last=Sato |title=Inflating Horizon of Particle Astrophysics and Cosmology |pages=astro–ph/0511743 |publisher=Universal Academy Press |date=2005 |isbn=978-4-946443-94-7 |arxiv=astro-ph/0511743 |bibcode=2005astro.ph.11743C}}</ref>

Despite the early universe being extremely [[density|dense]], it did not re-collapse into a black hole during the Big Bang, since the expansion rate was greater than the attraction. Following [[inflation theory]], general relativity predicts that the gravitational field slows the expansion of the universe.The negative pressure overcomes the positive energy density to produce a net repulsive gravitational field.<ref>{{Cite web |last=Guth |first=Alan |date=1997 |title=Was Cosmic Inflation the 'Bang' of the Big Bang? - A. Guth |url=https://ned.ipac.caltech.edu/level5/Guth/Guth3.html |access-date=2025-07-02 |website=NASA/IPAC Extragalactic Database (NED)}}</ref>

Models for the gravitational collapse of objects of relatively constant size, such as [[star]]s, do not necessarily apply in the same way to rapidly expanding space such as the Big Bang.<ref>{{cite web |author1=Philip Gibbs |title=Is the Big Bang a black hole? |url=http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/universe.html |publisher=[[John Baez]] |access-date=16 March 2018 |archive-date=31 December 2018 |archive-url=https://web.archive.org/web/20181231021714/http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/universe.html |url-status=live }}</ref>

=== High-energy collisions ===
Gravitational collapse is not the only process that could create black holes. In principle, black holes could be formed in [[high-energy physics|high-energy]] collisions that achieve sufficient density. As of 2002, no such events have been detected, either directly or indirectly as a deficiency of the mass balance in [[particle accelerator]] experiments.<ref>{{Cite journal |last1=Giddings |first1=S. B. |last2=Thomas |first2=S. |title=High energy colliders as black hole factories: The end of short distance physics |date=2002 |journal=Physical Review D |volume=65 |issue=5 |page=056010 |doi=10.1103/PhysRevD.65.056010 |arxiv=hep-ph/0106219|bibcode=2002PhRvD..65e6010G|s2cid=1203487 }}</ref> This suggests that there must be a lower limit for the mass of black holes. Theoretically, this boundary is expected to lie around the Planck mass, where quantum effects are expected to invalidate the predictions of general relativity.<ref>{{cite journal |last1=Harada |first1=T. |title=Is there a black hole minimum mass? |journal=Physical Review D |volume=74 |issue=8 |article-number=084004 |date=2006 |doi=10.1103/PhysRevD.74.084004 |arxiv=gr-qc/0609055 |bibcode=2006PhRvD..74h4004H |s2cid=119375284}}</ref>

This would put the creation of black holes firmly out of reach of any high-energy process occurring on or near the Earth. However, certain developments in quantum gravity suggest that the minimum black hole mass could be much lower: some [[braneworld]] scenarios for example put the boundary as low as {{val|1|u=TeV/c2}}.<ref>{{Cite journal |last1=Arkani–Hamed |first1=N. |last2=Dimopoulos |first2=S. |last3=Dvali |first3=G. |title=The hierarchy problem and new dimensions at a millimeter |journal=Physics Letters B |volume=429 |issue=3–4 |pages=263–272 |date=1998 |arxiv=hep-ph/9803315 |doi=10.1016/S0370-2693(98)00466-3|bibcode=1998PhLB..429..263A|s2cid=15903444 }}</ref> This would make it conceivable for [[micro black hole]]s to be created in the high-energy collisions that occur when [[cosmic ray]]s hit the Earth's atmosphere, or possibly in the [[Large Hadron Collider]] at [[CERN]]. These theories are very speculative, and the creation of black holes in these processes is deemed unlikely by many specialists.<ref name="LHCsafety">{{cite journal |url=http://lsag.web.cern.ch/lsag/LSAG-Report.pdf |title=Review of the Safety of LHC Collisions |journal=Journal of Physics G: Nuclear Physics |volume=35 |issue=11 |page=115004 |author=LHC Safety Assessment Group |url-status=live |archive-url=https://web.archive.org/web/20100414160742/http://lsag.web.cern.ch/lsag/LSAG-Report.pdf |archive-date=14 April 2010 |bibcode=2008JPhG...35k5004E |year=2008 |arxiv=0806.3414 |doi=10.1088/0954-3899/35/11/115004|s2cid=53370175 }}</ref> Even if micro black holes could be formed, it is expected that they would [[black hole evaporation|evaporate]] in about 10{{sup|−25}} seconds, posing no threat to the Earth.<ref>{{cite journal |last=Cavaglià |first=M. |title=Particle accelerators as black hole factories? |journal=Einstein-Online |volume=4 |page=1010 |date=2010 |url=http://www.einstein-online.info/spotlights/accelerators_bh/|archive-url=https://web.archive.org/web/20130508085759/http://www.einstein-online.info/spotlights/accelerators_bh |archive-date=8 May 2013 |access-date=8 May 2013}}</ref>

=== Growth ===
[[File:BBH gravitational lensing of gw150914.webm|alt=A simulation of two black holes colliding to form a super massive black hole|thumb|Simulation of two black holes colliding]]

Once a black hole has formed, it can continue to grow by absorbing additional [[matter]]. Any black hole will continually absorb gas and [[interstellar dust]] from its surroundings. This growth process is one possible way through which some supermassive black holes may have been formed, although the [[Supermassive black hole#Formation|formation of supermassive black holes]] is still an open field of research.<ref name="ReesVolonteri" /> A similar process has been suggested for the formation of [[intermediate-mass black hole]]s found in [[globular cluster]]s.<ref>{{cite journal |first1=E. |last1=Vesperini |first2=S. L. W. |last2=McMillan |first3=A. |last3=d'Ercole |first4=F. |last4=d'Antona |display-authors=3 |title=Intermediate-Mass Black Holes in Early Globular Clusters |journal=The Astrophysical Journal Letters |volume=713 |issue=1 |pages=L41–L44 |date=2010 |doi=10.1088/2041-8205/713/1/L41 |arxiv=1003.3470 |bibcode=2010ApJ...713L..41V |s2cid=119120429}}</ref> Black holes can also merge with other objects such as stars or even other black holes. This is thought to have been important, especially in the early growth of supermassive black holes, which could have formed from the aggregation of many smaller objects.<ref name="ReesVolonteri" /> The process has also been proposed as the origin of some intermediate-mass black holes.<ref>{{cite journal |last1=Zwart |first1=S. F. P. |last2=Baumgardt |first2=H. |last3=Hut |first3=P. |last4=Makino |first4=J. |last5=McMillan |first5=S. L. W. |display-authors=3 |title=Formation of massive black holes through runaway collisions in dense young star clusters |journal=Nature |volume=428 |issue=6984 |date=2004 |doi=10.1038/nature02448 |pmid=15085124 |arxiv=astro-ph/0402622 |bibcode=2004Natur.428..724P |pages=724–726 |s2cid=4408378}}</ref><ref>{{cite journal |last1=O'Leary |first1=R. M. |last2=Rasio |first2=F. A. |last3=Fregeau |first3=J. M. |last4=Ivanova |first4=N. |last5=o'Shaughnessy |first5=R. |display-authors=3 |title=Binary Mergers and Growth of Black Holes in Dense Star Clusters |journal=The Astrophysical Journal |volume=637 |issue=2 |pages=937–951 |date=2006 |doi=10.1086/498446 |arxiv=astro-ph/0508224 |bibcode=2006ApJ...637..937O |s2cid=1509957}}</ref>

=== Evaporation ===
{{Main|Hawking radiation}}

In 1974, Hawking predicted that black holes are not entirely black but emit small amounts of thermal radiation at a temperature ''ħc''{{sup|3}}/(8''πGM''[[Boltzmann constant|''k''{{sub|B}}]]);<ref name=Hawking1974>{{Cite journal |last=Hawking |first=S. W. |author-link1=Stephen Hawking |title=Black hole explosions? |journal=Nature |date=1974 |volume=248 |issue=5443 |pages=30–31 |doi=10.1038/248030a0|bibcode=1974Natur.248...30H|s2cid=4290107 }}</ref> this effect has become known as Hawking radiation. By applying quantum field theory to a static black hole background, he determined that a black hole should emit particles that display a perfect [[black body spectrum]]. Since Hawking's publication, many others have verified the result through various approaches.<ref>{{Cite journal |last=Page |first=D. N. |title=Hawking radiation and black hole thermodynamics |journal=New Journal of Physics |volume=7 |issue=1 |page=203 |date=2005 |arxiv=hep-th/0409024 |doi=10.1088/1367-2630/7/1/203|bibcode=2005NJPh....7..203P|s2cid=119047329 }}</ref> If Hawking's theory of black hole radiation is correct, then black holes are expected to shrink and evaporate over time as they lose mass by the emission of photons and other particles.<ref name=Hawking1974 /> The temperature of this thermal spectrum ([[Hawking temperature]]) is proportional to the surface gravity of the black hole, which, for a Schwarzschild black hole, is inversely proportional to the mass. Hence, large black holes emit less radiation than small black holes.<ref>{{harvnb|Carroll|2004|loc=Ch. 9.6}}</ref>

A stellar black hole of {{Solar mass|1}} has a Hawking temperature of 62&nbsp;[[nanokelvin]]s.<ref>{{cite news |last1=Siegel |first1=Ethan |author-link1=Ethan Siegel |title=Ask Ethan: Do Black Holes Grow Faster Than They Evaporate? |url=https://www.forbes.com/sites/startswithabang/2017/08/19/ask-ethan-do-black-holes-grow-faster-than-they-evaporate/ |access-date=17 March 2018 |work=Forbes ("Starts With A Bang" blog) |date=2017 |archive-date=22 November 2018 |archive-url=https://web.archive.org/web/20181122031830/https://www.forbes.com/sites/startswithabang/2017/08/19/ask-ethan-do-black-holes-grow-faster-than-they-evaporate/ |url-status=live }}</ref> This is far less than the 2.7&nbsp;K temperature of the [[cosmic microwave background]] radiation. Stellar-mass or larger black holes receive more mass from the cosmic microwave background than they emit through Hawking radiation and thus will grow instead of shrinking.<ref>{{cite journal |last1=Sivaram |first1=C. |title=Black hole Hawking radiation may never be observed! |journal=General Relativity and Gravitation |date=2001 |volume=33 |issue=2 |pages=175–181 |bibcode=2001GReGr..33..175S |doi=10.1023/A:1002753400430|s2cid=118913634 }}</ref> To have a Hawking temperature larger than 2.7&nbsp;K (and be able to evaporate), a black hole would need a mass less than the [[Moon]]. Such a black hole would have a diameter of less than a tenth of a millimetre.<ref>{{cite web |url=http://www.einstein-online.info/elementary/quantum/evaporating_bh/?set_language=en |title=Evaporating black holes? |website=Einstein online |publisher=Max Planck Institute for Gravitational Physics |date=2010 |access-date=12 December 2010 |archive-url=https://web.archive.org/web/20110722055345/http://www.einstein-online.info/elementary/quantum/evaporating_bh/?set_language=en |archive-date=22 July 2011}}</ref>

If a black hole is very small, the radiation effects are expected to become very strong. A black hole with the mass of a car would have a diameter of about 10{{sup|−24}}&nbsp;m and take a nanosecond to evaporate, during which time it would briefly have a luminosity of more than 200 times that of the Sun. Lower-mass black holes are expected to evaporate even faster; for example, a black hole of mass 1&nbsp;TeV/''c''{{sup|2}} would take less than 10{{sup|−88}} seconds to evaporate completely. For such a small black hole, quantum gravity effects are expected to play an important role and could hypothetically make such a small black hole stable, although current developments in quantum gravity do not indicate this is the case.<ref>{{cite journal |last1=Giddings |first1=S. B. |last2=Mangano |first2=M. L. |title=Astrophysical implications of hypothetical stable TeV-scale black holes |journal=Physical Review D |volume=78 |issue=3 |page=035009 |date=2008 |doi=10.1103/PhysRevD.78.035009 |arxiv=0806.3381 |bibcode=2008PhRvD..78c5009G |s2cid=17240525}}</ref><ref>{{cite journal |last1=Peskin |first1=M. E. |title=The end of the world at the Large Hadron Collider? |journal=Physics |volume=1 |article-number=14 |date=2008 |doi=10.1103/Physics.1.14 |bibcode=2008PhyOJ...1...14P|doi-access=free}}</ref>

The Hawking radiation for an astrophysical black hole is predicted to be very weak and would thus be exceedingly difficult to detect from Earth. A possible exception, however, is the burst of gamma rays emitted in the last stage of the evaporation of primordial black holes. Searches for such flashes have proven unsuccessful and provide stringent limits on the possibility of existence of low mass primordial black holes.<ref>{{Cite journal |last1=Fichtel |first1=C. E. |last2=Bertsch |first2=D. L. |last3=Dingus |first3=B. L.|author3-link= Brenda Dingus |last4=Esposito |first4=J. A. |last5=Hartman |first5=R. C. |last6=Hunter |first6=S. D. |last7=Kanbach |first7=G. |last8=Kniffen |first8=D. A. |last9=Lin |first9=Y. C. |display-authors=3 |title=Search of the energetic gamma-ray experiment telescope (EGRET) data for high-energy gamma-ray microsecond bursts |journal=Astrophysical Journal |volume=434 |issue=2 |pages=557–559 |date=1994 |doi=10.1086/174758|bibcode=1994ApJ...434..557F |last10=Mattox |first10=J. R. |last11=Mayer-Hasselwander |first11=H. A. |last12=McDonald |first12=L. |last13=Michelson |first13=P. F. |last14=Von Montigny |first14=C. |last15=Nolan |first15=P. L. |last16=Schneid |first16=E. J. |last17=Sreekumar |first17=P. |last18=Thompson |first18=D. J.}}</ref> NASA's [[Fermi Gamma-ray Space Telescope]] launched in 2008 will continue the search for these flashes.<ref>{{cite web |first=R. |last=Naeye |title=Testing Fundamental Physics |url=http://www.nasa.gov/mission_pages/GLAST/science/testing_fundamental_physics.html |publisher=NASA |access-date=16 September 2008 |url-status=live |archive-url=https://web.archive.org/web/20080831045232/http://www.nasa.gov/mission_pages/GLAST/science/testing_fundamental_physics.html |archive-date=31 August 2008}}</ref>

If black holes evaporate via Hawking radiation, a solar mass black hole will evaporate (beginning once the temperature of the cosmic microwave background drops below that of the black hole) over a period of 10{{sup|64}} years.<ref name="Frautschi1982" /> A supermassive black hole with a mass of {{Solar mass|{{10^|11}}}} will evaporate in around 2×10{{sup|100}} years.<ref name=page>{{cite journal | doi = 10.1103/PhysRevD.13.198 | volume=13 | title=Particle emission rates from a black hole: Massless particles from an uncharged, nonrotating hole | year=1976 | journal=Physical Review D | pages=198–206 | last1 = Page | first1 = Don N.| issue=2 | bibcode=1976PhRvD..13..198P}}. See in particular equation (27).</ref> During the collapse of a supercluster of galaxies, supermassive black holes are predicted to grow to perhaps {{solar mass|{{10^|14}}}}. Even these would evaporate over a [[Chronology of the universe|timescale]] of up to 10{{sup|106}} years.<ref name="Frautschi1982">{{cite journal |last1=Frautschi |first1=S. |title=Entropy in an Expanding Universe |journal=Science |volume=217 |issue=4560 |year=1982 |pages=593–599 |doi=10.1126/science.217.4560.593 |pmid=17817517 |bibcode=1982Sci...217..593F|s2cid=27717447 }} See page 596: table{{nbsp}}1 and section "black hole decay" and previous sentence on that page.</ref>

== Observational evidence ==
By nature, black holes do not themselves emit any electromagnetic radiation other than the hypothetical Hawking radiation, so astrophysicists searching for black holes must generally rely on indirect observations. For example, a black hole's existence can sometimes be inferred by observing its gravitational influence on its surroundings.<ref>{{cite web|title=Black Holes {{!}} Science Mission Directorate|url=https://science.nasa.gov/astrophysics/focus-areas/black-holes|publisher=NASA|access-date=17 March 2018|archive-date=17 November 2017|archive-url=https://web.archive.org/web/20171117232123/https://science.nasa.gov/astrophysics/focus-areas/black-holes|url-status=live}}</ref>

=== Direct interferometry ===
[[File:A_view_of_the_M87_supermassive_black_hole_in_polarised_light.tif|thumb|A view of supermassive black hole [[M87*]] in polarised light]]
[[File:EHT_Saggitarius_A_black_hole.tif|thumb|[[Sagittarius A*]], the supermassive black hole in the center of the Milky Way]]
The [[Event Horizon Telescope]] (EHT) is an active program that directly observes the immediate environment of black holes' event horizons, such as the black hole at the centre of the Milky Way. In April 2017, EHT began observing the black hole at the centre of [[Messier 87]].<ref name="eht">{{cite web |url=https://eventhorizontelescope.org/galleries/2017-observations |title=April 2017 Observations |work=Event Horizon Telescope |access-date=11 April 2019 |archive-date=10 April 2019 |archive-url=https://web.archive.org/web/20190410223148/https://eventhorizontelescope.org/galleries/2017-observations |url-status=live }}</ref><ref name="NYT-20240124">{{cite news |last=Overbye |first=Dennis |author-link=Dennis Overbye |title=That Famous Black Hole Gets a Second Look - Repeated studies of the supermassive black hole in the galaxy Messier 87 confirm that it continues to act as Einstein's theory predicted it would. |url=https://www.nytimes.com/2024/01/24/science/space/black-holes-photography-m87.html |date=24 January 2024 |work=[[The New York Times]] |url-status=live |archive-url=https://archive.today/20240124200523/https://www.nytimes.com/2024/01/24/science/space/black-holes-photography-m87.html |archive-date=24 January 2024 |access-date=25 January 2024 }}</ref> "In all, eight radio observatories on six mountains and four continents observed the galaxy in Virgo on and off for 10 days in April 2017" to provide the data yielding the image in April 2019.<ref name=OverbyeApril2019>{{cite news |url=https://www.nytimes.com/2019/04/10/science/black-hole-picture.html |title=Darkness Visible, Finally: Astronomers Capture First Ever Image of a Black Hole |last=Overbye |first=Dennis |date=10 April 2019 |access-date=11 April 2019 |newspaper=The New York Times |archive-date=21 May 2019 |archive-url=https://web.archive.org/web/20190521020231/https://www.nytimes.com/2019/04/10/science/black-hole-picture.html |url-status=live }}</ref>

After two years of data processing, EHT released its first  image of a black hole, at the center of the Messier 87 galaxy.<ref>{{cite news |url=https://www.nytimes.com/video/science/space/100000006453594/first-image-black-hole.html |type=video |date=10 April 2019 |author=AP |newspaper=The New York Times |title=Astronomers Reveal the First Picture of a Black Hole |access-date=11 April 2019 |archive-date=22 May 2019 |archive-url=https://web.archive.org/web/20190522052307/https://www.nytimes.com/video/science/space/100000006453594/first-image-black-hole.html |url-status=live }}</ref><ref>{{Cite web |last=Doeleman |first=Shep |title=The Event Horizon Telescope: Imaging and Time-Resolving a Black Hole |url=https://www.youtube.com/watch?v=_yGSgUUYDQ8&t=46m50s |website=Physics @ Berkeley |date=4 April 2016 |time=46:50 |access-date=8 July 2016 |url-status=live |archive-url=https://web.archive.org/web/20161201115303/https://www.youtube.com/watch?v=_yGSgUUYDQ8&t=46m50s |archive-date=1 December 2016}}</ref> What is visible is not the black hole—which shows as black because of the loss of all light within this dark region. Instead, it is the gases at the edge of the event horizon, displayed as orange or red, that define the black hole.<ref name=GrossmanApril2019>{{cite news |url=https://www.sciencenews.org/article/black-hole-first-picture-event-horizon-telescope |title=The first picture of a black hole opens a new era of astrophysics |date=10 April 2019 |last1=Grossman |first1=Lisa |last2=Conover |first2=Emily |newspaper=Science News |access-date=11 April 2019 |archive-date=27 April 2019 |archive-url=https://web.archive.org/web/20190427192956/https://www.sciencenews.org/article/black-hole-first-picture-event-horizon-telescope |url-status=live }}</ref>

On 12 May 2022, the EHT released the first image of [[Sagittarius A*]], the supermassive black hole at the centre of the Milky Way galaxy. The published image displayed the same ring-like structure and "shadow" seen in the M87* black hole. The boundary of the shadow or area of less brightness matches the predicted gravitationally lensed photon orbits.<ref>{{Cite journal |last1=Event Horizon Telescope Collaboration |last2=Akiyama |first2=Kazunori |last3=Alberdi |first3=Antxon |last4=Alef |first4=Walter |last5=Algaba |first5=Juan Carlos |last6=Anantua |first6=Richard |last7=Asada |first7=Keiichi |last8=Azulay |first8=Rebecca |last9=Bach |first9=Uwe |last10=Baczko |first10=Anne-Kathrin |last11=Ball |first11=David |last12=Baloković |first12=Mislav |last13=Barrett |first13=John |last14=Bauböck |first14=Michi |last15=Benson |first15=Bradford A. |date=2022-05-01 |title=First Sagittarius A* Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole in the Center of the Milky Way |journal=The Astrophysical Journal Letters |volume=930 |issue=2 |quote=The ring usually lies near the gravitationally lensed photon orbits that define the boundary of what we hereafter refer to as the black hole "shadow." |pages=L12 |doi=10.3847/2041-8213/ac6674 |doi-access=free |bibcode=2022ApJ...930L..12E |issn=2041-8205|arxiv=2311.08680 }}</ref> The image was created using the same techniques as for the M87 black hole. The imaging process for Sagittarius A*, which is more than a thousand times smaller and less massive than M87*, was significantly more complex because of the instability of its surroundings.<ref>{{CC-notice|by4}} {{Cite web |title=Astronomers Reveal First Image of the Black Hole at the Heart of Our Galaxy |url=https://eventhorizontelescope.org/blog/astronomers-reveal-first-image-black-hole-heart-our-galaxy |access-date=22 June 2022 |website=eventhorizontelescope.org |date=12 May 2022 |language=en}}</ref> The image of Sagittarius A* was partially blurred by turbulent [[Plasma (physics)|plasma]] on the way to the galactic centre, an effect which prevents resolution of the image at longer wavelengths.<ref>{{Cite journal |last=C. Bower |first=Geoffrey |date=May 2022 |title=Focus on First Sgr A* Results from the Event Horizon Telescope |url=https://iopscience.iop.org/journal/2041-8205/page/Focus_on_First_Sgr_A_Results |journal= The Astrophysical Journal Letters  |volume= |issue=2041–8205}}</ref>

The brightening of this material in the 'bottom' half of the processed EHT image is thought to be caused by [[Relativistic beaming|Doppler beaming]], whereby material approaching the viewer at relativistic speeds is perceived as brighter than material moving away. In the case of a black hole, this phenomenon implies that the visible material is rotating at relativistic speeds (>{{Convert|1,000|km/s|mph|abbr=on|disp=sqbr}}), the only speeds at which it is possible to centrifugally balance the immense gravitational attraction of the singularity, and thereby remain in orbit above the event horizon. This configuration of bright material implies that the EHT observed [[M87*]] from a perspective catching the black hole's accretion disc nearly edge-on, as the whole system rotated clockwise.<ref>{{Cite journal|last=Event Horizon Telescope Collaboration|title=First M87 Event Horizon Telescope Results. VII. Polarization of the Ring|journal=The Astrophysical Journal|year=2021|volume=910|issue=1|page=L12|doi=10.3847/2041-8213/abe71d|arxiv=2105.01169|bibcode=2021ApJ...910L..12E|s2cid=233851995|doi-access=free }}</ref><ref name=GrossmanApril2019/>

The extreme gravitational lensing associated with black holes produces the illusion of a perspective that sees the accretion disc from above. In reality, most of the ring in the EHT image was created when the light emitted by the far side of the accretion disc bent around the black hole's gravity well and escaped, meaning that most of the possible perspectives on M87* can see the entire disc, even that directly behind the "shadow".

In 2015, the EHT detected magnetic fields just outside the event horizon of Sagittarius A* and even discerned some of their properties. The field lines that pass through the accretion disc were a complex mixture of ordered and tangled. Theoretical studies of black holes had predicted the existence of magnetic fields.<ref>{{Cite journal |title=Resolved magnetic-field structure and variability near the event horizon of Sagittarius A* |journal=Science |date=4 December 2015 |pages=1242–1245 |volume=350 |issue=6265 |doi=10.1126/science.aac7087 |first1=M. D. |last1=Johnson |first2=V. L. |last2=Fish |first3=S. S. |last3=Doeleman |first4=D. P. |last4=Marrone |first5=R. L. |last5=Plambeck |first6=J. F. C. |last6=Wardle |first7=K. |last7=Akiyama |first8=K. |last8=Asada |first9=C. |last9=Beaudoin |arxiv=1512.01220 |bibcode=2015Sci...350.1242J |pmid=26785487|s2cid=21730194 }}</ref><ref>{{Cite web |title=Event Horizon Telescope Reveals Magnetic Fields at Milky Way's Central Black Hole |url=https://www.cfa.harvard.edu/news/2015-28 |website=cfa.harvard.edu |access-date=12 January 2016 |date=3 December 2015 |url-status=live |archive-url=https://web.archive.org/web/20151231211408/https://www.cfa.harvard.edu/news/2015-28 |archive-date=31 December 2015}}</ref>

In April 2023, an image of the shadow of the Messier 87 black hole and the related high-energy jet, viewed together for the first time, was presented.<ref name="NYT-20230426">{{cite news |last=Overbye |first=Dennis |author-link=Dennis Overbye |title=A Fresh View of an Increasingly Familiar Black Hole - Radio astronomers have captured a wide-angle image of one of the most violent locales in the cosmos. |url=https://www.nytimes.com/2023/04/26/science/astronomy-black-hole-m87.html |date=26 April 2023 |work=[[The New York Times]] |url-status=live |archive-url=https://archive.today/20230426212932/https://www.nytimes.com/2023/04/26/science/astronomy-black-hole-m87.html  |archive-date=26 April 2023 |access-date=26 April 2023 }}</ref><ref name="NAT-20230426">{{cite journal |author=Lu, Ru-Sen |display-authors=et al |title=A ring-like accretion structure in M87 connecting its black hole and jet |date=26 April 2023 |journal=[[Nature (journal)|Nature]] |volume=616 |issue=7958 |pages=686–690 |doi=10.1038/s41586-023-05843-w |pmid=37100940 |pmc=10132962 |arxiv=2304.13252 |bibcode=2023Natur.616..686L }}</ref>

=== Detection of gravitational waves from merging black holes ===
[[File:LIGO measurement of gravitational waves.svg|thumb|LIGO measurement of the gravitational waves at the Livingston (right) and Hanford (left) detectors, compared with the theoretical predicted values]]
On 14 September 2015, the [[LIGO]] gravitational wave observatory made the first-ever successful [[first observation of gravitational waves|direct observation of gravitational waves]].<ref name="PRL-20160211">{{cite journal |author=Abbott, B.P. |title=Observation of Gravitational Waves from a Binary Black Hole Merger |journal=[[Phys. Rev. Lett.]] |volume=116 |issue=6 |article-number=061102 |year=2016 |doi=10.1103/PhysRevLett.116.061102 |display-authors=etal |arxiv=1602.03837 |bibcode=2016PhRvL.116f1102A |pmid=26918975|s2cid=124959784 }}</ref><ref name="NYT-20160211-db">{{cite news |last=Overbye |first=Dennis |author-link=Dennis Overbye |title=Physicists Detect Gravitational Waves, Proving Einstein Right |url=https://www.nytimes.com/2016/02/12/science/ligo-gravitational-waves-black-holes-einstein.html |date=11 February 2016 |work=[[The New York Times]] |access-date=11 February 2016 |url-status=live |archive-url=https://web.archive.org/web/20160211165128/http://www.nytimes.com/2016/02/12/science/ligo-gravitational-waves-black-holes-einstein.html |archive-date=11 February 2016}}</ref> The signal was consistent with theoretical predictions for the gravitational waves produced by the merger of two black holes: one with about 36 solar masses, and the other around 29 solar masses.<ref name="PRL-20160211" /><ref name="Properties">{{cite journal |collaboration=[[LIGO Scientific Collaboration]] & [[Virgo interferometer|Virgo Collaboration]] |last1=Abbott |first1=Benjamin P. |arxiv=1602.03840 |title=Properties of the binary black hole merger GW150914 |journal=Physical Review Letters |volume=116 |issue=24 |article-number=241102 |date=11 February 2016 |bibcode=2016PhRvL.116x1102A |doi=10.1103/PhysRevLett.116.241102 |pmid=27367378|s2cid=217406416 }}</ref> This observation provides the most concrete evidence for the existence of black holes to date. For instance, the gravitational wave signal suggests that the separation of the two objects before the merger was just 350&nbsp;km, or roughly four times the Schwarzschild radius corresponding to the inferred masses. The objects must therefore have been extremely compact, leaving black holes as the most plausible interpretation.<ref name="PRL-20160211" />

More importantly, the signal observed by LIGO also included the start of the post-merger [[Binary black hole#Ringdown|ringdown]], the signal produced as the newly formed compact object settles down to a stationary state. Arguably, the ringdown is the most direct way of observing a black hole.<ref name="Cardoso2016">{{cite journal |author1=Cardoso, V. |author2=Franzin, E. |author3=Pani, P. |title=Is the gravitational-wave ringdown a probe of the event horizon? |doi=10.1103/PhysRevLett.116.171101 |pmid=27176511 |journal=[[Physical Review Letters]] |arxiv=1602.07309 |year=2016 |volume=116 |issue=17 |page=171101 |bibcode=2016PhRvL.116q1101C|s2cid=206273829 }}</ref> From the LIGO signal, it is possible to extract the frequency and damping time of the dominant mode of the ringdown. From these, it is possible to infer the mass and angular momentum of the final object, which match independent predictions from numerical simulations of the merger.<ref name="tests">{{cite journal |url=https://dcc.ligo.org/P1500213/public |title=Tests of general relativity with GW150914 |collaboration=[[LIGO Scientific Collaboration]] & [[Virgo interferometer|Virgo Collaboration]] |last1=Abbott |first1=Benjamin P. |journal=Physical Review Letters |date=11 February 2016 |volume=116 |issue=22 |article-number=221101 |doi=10.1103/PhysRevLett.116.221101 |pmid=27314708 |arxiv=1602.03841 |bibcode=2016PhRvL.116v1101A |s2cid=217275338 |access-date=12 February 2016 |archive-url=https://web.archive.org/web/20160215165039/https://dcc.ligo.org/P1500213/public |archive-date=15 February 2016 }}</ref> The frequency and decay time of the dominant mode are determined by the geometry of the photon sphere. Hence, observation of this mode confirms the presence of a photon sphere; however, it cannot exclude possible exotic alternatives to black holes that are compact enough to have a photon sphere.<ref name="Cardoso2016"/><ref name="Murk2023">{{cite journal |last=Murk |first=Sebastian |title=Nomen non est omen: Why it is too soon to identify ultra-compact objects as black holes |journal=International Journal of Modern Physics D |year=2023 |volume=32 |issue=14 |pages=2342012–2342235 |article-number=2342012 |doi=10.1142/S0218271823420129 |arxiv=2210.03750 |bibcode=2023IJMPD..3242012M |s2cid=252781040}}</ref>

The observation also provides the first observational evidence for the existence of stellar-mass black hole binaries. Furthermore, it is the first observational evidence of stellar-mass black holes weighing 25 solar masses or more.<ref name="implications">{{cite journal |collaboration=[[LIGO Scientific Collaboration]] & [[Virgo interferometer|Virgo Collaboration]] |title=Astrophysical Implications of the Binary Black Hole Merger GW150914 |doi=10.3847/2041-8205/818/2/L22 |journal=Astrophys. J. Lett. |volume=818 |number=2 |page=L22 |url=https://dcc.ligo.org/P1500262/public |arxiv=1602.03846 |bibcode=2016ApJ...818L..22A |year=2016 |last1=Abbott |first1=B. P. |hdl=1826/11732 |s2cid=209315965 |url-status=live |archive-url=https://web.archive.org/web/20160316053938/https://dcc.ligo.org/P1500262/public |archive-date=16 March 2016 |doi-access=free }}</ref>

Since then, many more [[List of gravitational wave observations|gravitational wave events]] have been observed.<ref name="ligo list">{{cite web|title=Detection of gravitational waves|url=https://www.ligo.org/detections.php|access-date=9 April 2018|publisher=[[LIGO]]|archive-date=20 May 2020|archive-url=https://web.archive.org/web/20200520134427/https://www.ligo.org/detections.php|url-status=live}}</ref>

=== Stars orbiting Sagittarius A* ===
{{Main|Sagittarius A* cluster}}
[[File:SgrA2021.gif|thumb|Stars moving around Sagittarius A* as seen in 2021]]
The [[proper motion]]s of stars near the centre of our own Milky Way provide strong observational evidence that these stars are orbiting a supermassive black hole.<ref name="Gillessen">{{cite journal |last1=Gillessen |first1=S. |last2=Eisenhauer |first2=F. |last3=Trippe |first3=S. |last4=Alexander |first4=T. |last5=Genzel |first5=R. |last6=Martins |first6=F. |last7=Ott |first7=T. |display-authors=3 |title=Monitoring Stellar Orbits around the Massive Black Hole in the Galactic Center |journal=The Astrophysical Journal |volume=692 |issue=2 |pages=1075–1109 |date=2009 |doi=10.1088/0004-637X/692/2/1075 |arxiv=0810.4674 |bibcode=2009ApJ...692.1075G |s2cid=1431308}}</ref> Since 1995, astronomers have tracked the motions of 90 stars orbiting an invisible object coincident with the radio source Sagittarius A*. By fitting their motions to [[Keplerian orbit]]s, the astronomers were able to infer, in 1998, that a {{Solar mass|{{val|2.6e6}}}} object must be contained in a volume with a radius of 0.02 [[light-year]]s to cause the motions of those stars.<ref name="Ghez1998">{{cite journal |last1=Ghez |first1=A. M. |last2=Klein |first2=B. L. |last3=Morris |first3=M. |last4=Becklin |first4=E. E. |display-authors=3 |title=High Proper-Motion Stars in the Vicinity of Sagittarius A*: Evidence for a Supermassive Black Hole at the Center of Our Galaxy |journal=The Astrophysical Journal |volume=509 |issue=2 |pages=678–686 |date=1998 |doi=10.1086/306528 |arxiv=astro-ph/9807210 |bibcode=1998ApJ...509..678G |s2cid=18243528}}</ref>

Since then, one of the stars—called [[S2 (star)|S2]]—has completed a full orbit. From the orbital data, astronomers were able to refine the calculations of the mass to {{Solar mass|{{val|4.3e6}}}} and a radius of less than 0.002 light-years for the object causing the orbital motion of those stars.<ref name="Gillessen" /> The upper limit on the object's size is still too large to test whether it is smaller than its Schwarzschild radius. Nevertheless, these observations strongly suggest that the central object is a supermassive black hole as there are no other plausible scenarios for confining so much invisible mass into such a small volume.<ref name="Ghez1998" /> Additionally, there is some observational evidence that this object might possess an event horizon, a feature unique to black holes.<ref>{{Cite journal |title=The Event Horizon of Sagittarius A* |last1=Broderick |first1=Avery |date=August 2009 |journal=The Astrophysical Journal |doi=10.1088/0004-637X/701/2/1357 |last2=Loeb |first2=Abraham |last3=Narayan |first3=Ramesh |volume=701 |issue=2 |pages=1357–1366 |arxiv=0903.1105 |bibcode=2009ApJ...701.1357B|s2cid=12991878 }}</ref>

=== Accretion of matter ===
{{See also|Accretion disk}}
[[File:PIA18467-NuSTAR-Plot-BlackHole-BlursLight-20140812.png|thumb|Blurring of X-rays near black hole ([[NuSTAR]]; 12 August 2014)<ref name="NASA-20140812">{{cite web |author=<!--Staff writer(s); no by-line.--> |date=12 August 2014 |title=NASA's NuSTAR Sees Rare Blurring of Black Hole Light |url=http://www.jpl.nasa.gov/news/news.php?release=2014-273 |archive-url=https://web.archive.org/web/20140813072002/http://www.jpl.nasa.gov/news/news.php?release=2014-273 |archive-date=13 August 2014 |access-date=12 August 2014 |website=[[NASA]]}}</ref>]]

Due to [[conservation of angular momentum]],<ref>{{Cite news|url=https://phys.org/news/2018-02-dynamics-black-hole-rotational-energy.html|title=Researchers clarify dynamics of black hole rotational energy|access-date=17 September 2018|archive-date=17 September 2018|archive-url=https://web.archive.org/web/20180917105330/https://phys.org/news/2018-02-dynamics-black-hole-rotational-energy.html|url-status=live}}</ref> gas falling into the [[gravitational well]] created by a massive object will typically form a disk-like structure around the object. Artists' impressions such as the accompanying representation of a black hole with corona commonly depict the black hole as if it were a flat-space body hiding the part of the disk just behind it, but in reality gravitational lensing would greatly distort the image of the accretion disk.<ref>{{cite journal |last=Marck |first=Jean-Alain |title=Short-cut method of solution of geodesic equations for Schwarzchild black hole |journal=Classical and Quantum Gravity |volume=13 |issue=3 |date=1 March 1996 |issn=0264-9381 |doi=10.1088/0264-9381/13/3/007 |pages=393–402 |arxiv=gr-qc/9505010|bibcode=1996CQGra..13..393M|s2cid=119508131 }}</ref>

Within such a disk, friction would cause angular momentum to be transported outward, allowing matter to fall farther inward, thus releasing potential energy and increasing the temperature of the gas.<ref name=McClintockRemillard2006>{{Cite book |last1=McClintock |first1=J. E. |last2=Remillard |first2=R. A. |chapter=Black Hole Binaries |editor1-first=W. |editor1-last=Lewin|editor2-first=M. |editor2-last=van der Klis |title=Compact Stellar X-ray Sources |page=157 |date=2006 |isbn=978-0-521-82659-4 |arxiv=astro-ph/0306213 |bibcode=2006csxs.book..157M}} section 4.1.5.</ref>

When the accreting object is a neutron star or a black hole, the gas in the inner accretion disk orbits at very high speeds because of its proximity to the [[compact object]]. The resulting friction is so significant that it heats the inner disk to temperatures at which it emits vast amounts of electromagnetic radiation (mainly [[X-ray]]s). These bright X-ray sources may be detected by telescopes. This process of accretion is one of the most efficient energy-producing processes known. Up to 40% of the rest mass of the accreted material can be emitted as radiation.<ref name=McClintockRemillard2006 /> In nuclear fusion only about 0.7% of the rest mass will be emitted as energy. In many cases, accretion disks are accompanied by [[relativistic jets]] that are emitted along the poles, which carry away much of the energy. The mechanism for the creation of these jets is currently not well understood, in part due to insufficient data.<ref>{{cite news |title=What powers a black hole's mighty jets? |url=https://www.science.org/content/article/what-powers-black-holes-mighty-jets |access-date=19 March 2018 |work=Science {{!}} AAAS |date=19 November 2014 |archive-date=5 May 2019 |archive-url=https://web.archive.org/web/20190505171217/https://www.sciencemag.org/news/2014/11/what-powers-black-holes-mighty-jets |url-status=live }}</ref>

As such, many of the universe's more energetic phenomena have been attributed to the accretion of matter on black holes. In particular, active galactic nuclei and [[quasar]]s are believed to be the accretion disks of supermassive black holes.<ref name="CMS1999" /> Similarly, X-ray binaries are generally accepted to be [[binary star]] systems in which one of the two stars is a compact object accreting matter from its companion.<ref name="CMS1999" /> It has also been suggested that some [[ultraluminous X-ray source]]s may be the accretion disks of intermediate-mass black holes.<ref>{{Cite journal |last1=Winter |first1=L. M. |last2=Mushotzky |first2=R. F. |last3=Reynolds |first3=C. S. |title=XMM-Newton Archival Study of the Ultraluminous X-Ray Population in Nearby Galaxies |date=2006 |journal=The Astrophysical Journal |volume=649 |issue=2 |pages=730–752 |arxiv=astro-ph/0512480 |doi=10.1086/506579|bibcode=2006ApJ...649..730W|s2cid=118445260 }}</ref>

Stars have been observed to get torn apart by tidal forces in the immediate vicinity of supermassive black holes in galaxy nuclei, in what is known as a [[tidal disruption event | tidal disruption event (TDE)]]. Some of the material from the disrupted star forms an accretion disk around the black hole, which emits observable electromagnetic radiation.

In November 2011 the first direct observation of a quasar accretion disk around a supermassive black hole was reported.<ref>{{Cite web |url=https://www.spacetelescope.org/news/heic1116/ |title=Hubble directly observes the disk around a black hole |last=information@eso.org |website=www.spacetelescope.org |access-date=7 March 2016 |url-status=live |archive-url=https://web.archive.org/web/20160308001224/http://spacetelescope.org/news/heic1116/ |archive-date=8 March 2016}}</ref><ref>{{Cite journal |last1=Muñoz |first1=José A. |last2=Mediavilla |first2=Evencio |last3=Kochanek |first3=Christopher S. |last4=Falco |first4=Emilio |last5=Mosquera |first5=Ana María |date=1 December 2011 |title=A Study of Gravitational Lens Chromaticity with the Hubble Space Telescope |journal=The Astrophysical Journal |volume=742 |issue=2 |page=67 |doi=10.1088/0004-637X/742/2/67 |arxiv=1107.5932 |bibcode=2011ApJ...742...67M|s2cid=119119359 }}</ref>

==== X-ray binaries ====
{{See also|X-ray binary}}
[[File:Chandra image of Cygnus X-1.jpg|thumb|A [[Chandra X-Ray Observatory]] image of [[Cygnus X-1]], which was the first strong black hole candidate discovered]]

[[X-ray binaries]] are binary star systems that emit a majority of their radiation in the [[X-ray]] part of the spectrum. These X-ray emissions are generally thought to result when one of the stars (compact object) accretes matter from another (regular) star. The presence of an ordinary star in such a system provides an opportunity for studying the central object and to determine if it might be a black hole.<ref name="CMS1999" />

If such a system emits signals that can be directly traced back to the compact object, it cannot be a black hole. The absence of such a signal does, however, not exclude the possibility that the compact object is a neutron star. By studying the companion star it is often possible to obtain the orbital parameters of the system and to obtain an estimate for the mass of the compact object. If this is much larger than the Tolman–Oppenheimer–Volkoff limit (the maximum mass a star can have without collapsing) then the object cannot be a neutron star and is generally expected to be a black hole.<ref name="CMS1999">{{Cite journal |last1=Celotti |first1=A. |last2=Miller |first2=J. C. |last3=Sciama |first3=D. W. |title=Astrophysical evidence for the existence of black holes |journal=Classical and Quantum Gravity |volume=16 |issue=12A |pages=A3–A21 |date=1999 |arxiv=astro-ph/9912186 |doi=10.1088/0264-9381/16/12A/301 |url=https://cds.cern.ch/record/411555/files/9912186.pdf |bibcode=1999CQGra..16A...3C |s2cid=17677758 |access-date=27 July 2018 |archive-date=27 July 2018 |archive-url=https://web.archive.org/web/20180727052939/https://cds.cern.ch/record/411555/files/9912186.pdf |url-status=live }}</ref>

The first strong candidate for a black hole, [[Cygnus X-1]], was discovered in this way by [[Charles Thomas Bolton]],<ref name="Bolton1972"/> [[Louise Webster]], and [[Paul Murdin]]<ref name="Webster1972"/> in 1972.<ref>{{cite web |last=Rolston |first=B. |date=10 November 1997 |url=http://news.utoronto.ca/bin/bulletin/nov10_97/art4.htm |archive-url=https://web.archive.org/web/20080502230214/http://news.utoronto.ca/bin/bulletin/nov10_97/art4.htm |archive-date=2 May 2008 |title=The First Black Hole |website=The bulletin |publisher=University of Toronto |access-date=11 March 2008}}</ref><ref name="Shipman1975"/> Some doubt remained, due to the uncertainties that result from the companion star being much heavier than the candidate black hole. Currently, better candidates for black holes are found in a class of X-ray binaries called soft X-ray transients. In this class of system, the companion star is of relatively low mass allowing for more accurate estimates of the black hole mass. These systems actively emit X-rays for only several months once every 10–50 years. During the period of low X-ray emission, called quiescence, the accretion disk is extremely faint, allowing detailed observation of the companion star during this period. One of the best such candidates is [[V404 Cygni]].<ref name="CMS1999" />

===== Quasi-periodic oscillations =====
{{Main|Quasi-periodic oscillation}}

The X-ray emissions from accretion disks sometimes flicker at certain frequencies. These signals are called [[quasi-periodic oscillation]]s and are thought to be caused by material moving along the inner edge of the accretion disk (the innermost stable circular orbit). As such their frequency is linked to the mass of the compact object. They can thus be used as an alternative way to determine the mass of candidate black holes.<ref>{{cite press release |title=NASA scientists identify smallest known black hole |publisher=[[Goddard Space Flight Center]] |date=1 April 2008 |url=http://www.eurekalert.org/pub_releases/2008-04/nsfc-nsi040108.php |access-date=14 March 2009 |archive-url=https://web.archive.org/web/20081227195554/http://www.eurekalert.org/pub_releases/2008-04/nsfc-nsi040108.php |archive-date=27 December 2008 }}</ref>

==== Galactic nuclei ====
{{See also|Active galactic nucleus}}
[[File:X-RayFlare-BlackHole-MilkyWay-20140105.jpg|thumb|Detection of unusually bright [[X-ray]] flare from Sagittarius A*, a black hole in the centre of the Milky Way galaxy on 5{{nbsp}}January 2015<ref name="NASA-20150105">{{cite web |last1=Chou |first1=Felicia |last2=Anderson |first2=Janet |last3=Watzke |first3=Megan |date=5 January 2015 |title=RELEASE 15-001 – NASA's Chandra Detects Record-Breaking Outburst from Milky Way's Black Hole |url=http://www.nasa.gov/press/2015/january/nasa-s-chandra-detects-record-breaking-outburst-from-milky-way-s-black-hole/ |url-status=live |archive-url=https://web.archive.org/web/20150106100532/http://www.nasa.gov/press/2015/january/nasa-s-chandra-detects-record-breaking-outburst-from-milky-way-s-black-hole/ |archive-date=6 January 2015 |access-date=6 January 2015 |website=[[NASA]]}}</ref>]]

Astronomers use the term "active galaxy" to describe galaxies with unusual characteristics, such as unusual [[spectral line]] emission and very strong radio emission. Theoretical and observational studies have shown that the activity in these active galactic nuclei (AGN) may be explained by the presence of supermassive black holes, which can be millions of times more massive than stellar ones. The models of these AGN consist of a central black hole that may be millions or billions of times more massive than the [[Sun]]; a disk of [[interstellar gas]] and dust called an accretion disk; and two [[relativistic jet|jets]] perpendicular to the accretion disk.<ref name="krolik1999">{{Cite book |first=J. H. |last=Krolik |date=1999 |title=Active Galactic Nuclei |publisher=Princeton University Press |isbn=978-0-691-01151-6 |at=Ch. 1.2 |url=https://books.google.com/books?id=oRK8otMiWIgC&q=Active+Galactic+Nuclei |access-date=16 October 2020 |archive-date=14 August 2021 |archive-url=https://web.archive.org/web/20210814220336/https://books.google.com/books?id=oRK8otMiWIgC&q=Active+Galactic+Nuclei |url-status=live }}</ref><ref name="sparkegallagher2000">{{Cite book |first1=L. S. |last1=Sparke |author-link=Linda Sparke |first2=J. S. |last2=Gallagher |date=2000 |title=Galaxies in the Universe: An Introduction |publisher=Cambridge University Press |at=Ch. 9.1 |url=https://books.google.com/books?id=N8Hngab5liQC&q=Galaxies+in+the+Universe:+An+Introduction |isbn=978-0-521-59740-1 |access-date=16 October 2020 |archive-date=22 March 2022 |archive-url=https://web.archive.org/web/20220322141933/https://books.google.com/books?id=N8Hngab5liQC&q=Galaxies+in+the+Universe%3A+An+Introduction |url-status=live }}</ref>

Although supermassive black holes are expected to be found in most AGN, only some galaxies' nuclei have been more carefully studied in attempts to both identify and measure the actual masses of the central supermassive black hole candidates. Some of the most notable galaxies with supermassive black hole candidates include the [[Andromeda Galaxy]], [[Messier 32|M32]], [[Messier 87|M87]], [[NGC 3115]], [[NGC 3377]], [[NGC 4258]], [[NGC 4889]], [[NGC 1277]], [[OJ 287]], [[APM 08279+5255]] and the [[Sombrero Galaxy]].<ref name="kormendyrichstone1995">{{Cite journal |first1=J. |last1=Kormendy |first2=D. |last2=Richstone |title=Inward Bound – The Search For Supermassive Black Holes In Galactic Nuclei |journal=Annual Review of Astronomy and Astrophysics |date=1995 |volume=33 |issue=1 |pages=581–624 |bibcode=1995ARA&A..33..581K |doi=10.1146/annurev.aa.33.090195.003053}}</ref>

It is now widely accepted that the centre of nearly every galaxy, not just active ones, contains a supermassive black hole.<ref name="King">{{Cite journal |last=King |first=A. |title=Black Holes, Galaxy Formation, and the MBH-σ Relation |journal=The Astrophysical Journal Letters |volume=596 |issue=1 |pages=27–29 |date=2003 |doi=10.1086/379143 |arxiv=astro-ph/0308342|bibcode=2003ApJ...596L..27K|s2cid=9507887 }}</ref> The close observational correlation between the mass of this hole and the velocity dispersion of the host galaxy's [[galactic bulge|bulge]], known as the [[M–sigma relation]], strongly suggests a connection between the formation of the black hole and that of the galaxy itself.<ref name="msigma2000">{{Cite journal |title=A Fundamental Relation Between Supermassive Black Holes and their Host Galaxies |last1=Ferrarese |first1=L. |last2=Merritt |first2=D. |author2-link=David Merritt |journal=The Astrophysical Journal Letters |volume=539 |issue=1 |pages=9–12 |date=2000 |bibcode=2000ApJ...539L...9F |doi=10.1086/312838 |arxiv=astro-ph/0006053 |s2cid=6508110}}</ref>

=== Microlensing ===
Another way the black hole nature of an object may be tested is through observation of effects caused by a strong gravitational field in their vicinity. One such effect is gravitational lensing: The deformation of spacetime around a massive object causes light rays to be deflected, such as light passing through an optic [[lens]]. Observations have been made of weak gravitational lensing, in which light rays are deflected by only a few [[arcsecond]]s. [[Microlensing]] occurs when the sources are unresolved and the observer sees a small brightening. The turn of the millennium saw the first 3 candidate detections of black holes in this way,<ref>{{Cite journal |last1=Bennett |first1=D. P. |last2=Becker |first2=A. C. |last3=Quinn |first3=J. L. |last4=Tomaney |first4=A. B. |last5=Alcock |first5=C. |last6=Allsman |first6=R. A. |last7=Alves |first7=D. R. |last8=Axelrod |first8=T. S. |last9=Calitz |first9=J. J. |last10=Cook |first10=K. H. |last11=Drake |first11=A. J. |last12=Fragile |first12=P. C. |last13=Freeman |first13=K. C. |last14=Geha |first14=M. |last15=Griest |first15=K. |date=2002-11-01 |title=Gravitational Microlensing Events Due to Stellar-Mass Black Holes |url=https://ui.adsabs.harvard.edu/abs/2002ApJ...579..639B/abstract |journal=The Astrophysical Journal |volume=579 |issue=2 |pages=639–659 |doi=10.1086/342225 |arxiv=astro-ph/0109467 |bibcode=2002ApJ...579..639B |issn=0004-637X}}</ref><ref>{{Cite journal |last1=Mao |first1=Shude |last2=Smith |first2=Martin C. |last3=Woźniak |first3=P. |last4=Udalski |first4=A. |last5=Szymański |first5=M. |last6=Kubiak |first6=M. |last7=Pietrzyński |first7=G. |last8=Soszyński |first8=I. |last9=Żebruń |first9=K. |date=2002-01-01 |title=Optical Gravitational Lensing Experiment OGLE-1999-BUL-32: the longest ever microlensing event - evidence for a stellar mass black hole? |journal=Monthly Notices of the Royal Astronomical Society |volume=329 |issue=2 |pages=349–354 |doi=10.1046/j.1365-8711.2002.04986.x |doi-access=free |arxiv=astro-ph/0108312 |bibcode=2002MNRAS.329..349M |issn=0035-8711}}</ref> and in January 2022, astronomers reported the first confirmed detection of a microlensing event from an isolated black hole.<ref name="Sahu">{{cite journal |arxiv=2201.13296 |last1=Sahu |first1=K. C. |title=An Isolated Stellar-Mass Black Hole Detected Through Astrometric Microlensing |journal=Astrophysical Journal|date=2022|volume=933 |issue=1 |page=83 |doi=10.3847/1538-4357/ac739e |bibcode=2022ApJ...933...83S |s2cid=246430448 |doi-access=free }}</ref>

Another possibility for observing gravitational lensing by a black hole would be to observe stars orbiting the black hole. There are several candidates for such an observation in orbit around [[Sagittarius A*]].<ref name="Bozza">{{cite journal |arxiv=0911.2187 |last1=Bozza |first1=V. |title=Gravitational Lensing by Black Holes |journal=General Relativity and Gravitation |issue=9 |date=2010 |pages=2269–2300 |doi=10.1007/s10714-010-0988-2 |bibcode=2010GReGr..42.2269B |volume=42 |s2cid=118635353}}</ref>

{{Clear}}

== Alternatives ==
{{See also|Exotic star}}

The evidence for stellar black holes strongly relies on the existence of an upper limit for the mass of a neutron star. The size of this limit heavily depends on the assumptions made about the properties of dense matter. New exotic [[Phase (matter)|phases of matter]] could push up this bound.<ref name="CMS1999" /> A phase of free [[quark]]s at high density might allow the existence of dense quark stars,<ref>{{cite journal |last1=Kovacs |first1=Z. |last2=Cheng |first2=K. S. |last3=Harko |first3=T. |title=Can stellar mass black holes be quark stars? |journal=[[Monthly Notices of the Royal Astronomical Society]] |date=2009 |volume=400 |issue=3 |pages=1632–1642 |doi=10.1111/j.1365-2966.2009.15571.x |doi-access=free |arxiv=0908.2672 |bibcode=2009MNRAS.400.1632K |s2cid=18263809}}</ref> and some [[supersymmetry|supersymmetric]] models predict the existence of [[Q star]]s.<ref>{{cite arXiv |eprint=hep-ph/0612159 |first1=A. |last1=Kusenko |title=Properties and signatures of supersymmetric Q-balls |date=2006 }}</ref> Some extensions of the [[standard model]] posit the existence of [[preon]]s as fundamental building blocks of quarks and [[lepton]]s, which could hypothetically form [[preon star]]s.<ref>{{cite journal |last1=Hansson |first1=J. |last2=Sandin |first2=F. |title=Preon stars: a new class of cosmic compact objects |journal=Physics Letters B |volume=616 |issue=1–2 |pages=1–7 |date=2005 |doi=10.1016/j.physletb.2005.04.034 |arxiv=astro-ph/0410417 |bibcode=2005PhLB..616....1H |s2cid=119063004}}</ref> These hypothetical models could potentially explain a number of observations of stellar black hole candidates. However, it can be shown from arguments in general relativity that any such object will have a maximum mass.<ref name="CMS1999" />

Since the average density of a black hole inside its Schwarzschild radius is inversely proportional to the square of its mass, supermassive black holes are much less dense than stellar black holes. The average density of a {{Solar mass|{{10^|8}}}} black hole is comparable to that of water.<ref name="CMS1999" /> Consequently, the physics of matter forming a supermassive black hole is much better understood and the possible alternative explanations for supermassive black hole observations are much more mundane. For example, a supermassive black hole could be modelled by a large cluster of very dark objects. However, such alternatives are typically not stable enough to explain the supermassive black hole candidates.<ref name="CMS1999" />

The evidence for the existence of stellar and supermassive black holes implies that in order for black holes not to form, general relativity must fail as a theory of gravity, perhaps due to the onset of [[quantum mechanics|quantum mechanical]] corrections. A much anticipated feature of a theory of quantum gravity is that it will not feature singularities or event horizons and thus black holes would not be real artefacts.<ref>{{cite journal |last1=Kiefer |first1=C. |title=Quantum gravity: general introduction and recent developments |journal=Annalen der Physik |volume=15 |issue=1–2 |pages=129–148 |date=2006 |doi=10.1002/andp.200510175 |arxiv=gr-qc/0508120 |bibcode=2006AnP...518..129K |s2cid=12984346}}</ref> For example, in the [[Fuzzball (string theory)|fuzzball]] model<ref>{{cite journal |last=Mathur |first=Samir D. |title=The fuzzball proposal for black holes: an elementary review |journal=Fortschritte der Physik |volume=53 |issue=7–8 |page=793 |date=2005 |doi=10.1002/prop.200410203 |arxiv=hep-th/0502050 |bibcode=2005ForPh..53..793M |s2cid=15083147}}</ref> based on [[string theory]], the individual states of a black hole solution do not generally have an event horizon or singularity, but for a classical/semiclassical observer the statistical average of such states appears just as an ordinary black hole as deduced from general relativity.<ref>{{cite journal |last1=Skenderis |first1=K. |last2=Taylor |first2=M. |title=The fuzzball proposal for black holes |journal=Physics Reports |volume=467 |issue=4–5 |page=117 |date=2008 |doi=10.1016/j.physrep.2008.08.001 |arxiv=0804.0552 |bibcode=2008PhR...467..117S |s2cid=118403957}}</ref>

A few theoretical objects have been conjectured to match observations of astronomical black hole candidates identically or near-identically,<ref name="Murk2023"/> but which function via a different mechanism. These include the [[gravastar]],<ref>{{cite journal |last1=Mazur |first1=Pawel O. |last2=Mottola |first2=Emil |title=Gravitational vacuum condensate stars |journal=Proceedings of the National Academy of Sciences of the United States of America |volume=101 |issue=26 |date=2004 |pages=9545–9550 |doi=10.1073/pnas.0402717101 |doi-access=free |pmid=15210982 |pmc=470711 |arxiv=gr-qc/0407075 |bibcode=2004PNAS..101.9545M |s2cid=2607263}}</ref> the [[black star (semiclassical gravity)|black star]],<ref>{{cite news |last1=Choi |first1=Charles Q. |title=Black Hole Pretenders Could Really Be Bizarre Quantum Stars |url=https://www.scientificamerican.com/article/black-hole-pretenders-could-really-be-bizarre-quantum-stars/ |access-date=17 March 2018 |work=Scientific American |date=2018 |archive-date=17 June 2019 |archive-url=https://web.archive.org/web/20190617164631/https://www.scientificamerican.com/article/black-hole-pretenders-could-really-be-bizarre-quantum-stars/ |url-status=live }}</ref> related [[nestar]]<ref name="SA-20240220">{{cite news |last=McRae |first=Mike |title=Bubble-Like 'Stars Within Stars' Could Explain Black Hole Weirdness |url=https://www.sciencealert.com/bubble-like-stars-within-stars-could-explain-black-hole-weirdness |date=20 February 2024 |work=[[ScienceAlert]] |url-status=live |archive-url=https://archive.today/20240220150012/https://www.sciencealert.com/bubble-like-stars-within-stars-could-explain-black-hole-weirdness |archive-date=20 February 2024 |access-date=20 February 2024 }}</ref> and the [[dark-energy star]].<ref>{{cite journal |last1=Ball |first1=Philip |title=Black holes 'do not exist' |journal=Nature |date=31 March 2005 |doi=10.1038/news050328-8}}</ref>

== Open questions ==
=== Entropy and thermodynamics ===
{{further|Black hole thermodynamics|Bekenstein bound}}
{{Image frame|content={{bigmath|1=''S'' = {{sfrac|1|4}} {{sfrac|''c''{{sup|3}}''k'' |''Għ''}} ''A''}}|caption=The formula for the Bekenstein–Hawking entropy ({{mvar|S}}) of a black hole, which depends on the area of the black hole ({{mvar|A}}). The constants are the [[speed of light]] ({{mvar|c}}), the [[Boltzmann constant]] ({{mvar|k}}), [[Newton's constant]] ({{mvar|G}}), and the [[reduced Planck constant]] ({{mvar|ħ}}). In Planck units, this reduces to {{math|1=''S'' = {{sfrac|''A''|4}}}}.|width=220}}

In 1971, Hawking showed under general conditions<ref group=Note>In particular, he assumed that all matter satisfies the [[weak energy condition]].</ref> that the total area of the event horizons of any collection of classical black holes can never decrease, even if they collide and merge.<ref>{{cite journal |last=Hawking |first=S. W. |title=Gravitational Radiation from Colliding Black Holes |journal=Physical Review Letters |volume=26 |issue=21 |pages=1344–1346 |date=1971 |doi=10.1103/PhysRevLett.26.1344 |bibcode=1971PhRvL..26.1344H}}</ref> This result, now known as the [[second law of black hole mechanics]], is remarkably similar to the [[second law of thermodynamics]], which states that the total entropy of an isolated system can never decrease. As with classical objects at [[absolute zero]] temperature, it was assumed that black holes had zero entropy. If this were the case, the second law of thermodynamics would be violated by entropy-laden matter entering a black hole, resulting in a decrease in the total entropy of the universe. Therefore, Bekenstein proposed that a black hole should have an entropy, and that it should be proportional to its horizon area.<ref name="wald99">{{cite journal |last=Wald |first=R. M. |title=The Thermodynamics of Black Holes |journal=Living Reviews in Relativity |volume=4 |issue=1 |article-number=6 |date=2001 |arxiv=gr-qc/9912119 |bibcode=2001LRR.....4....6W |doi=10.12942/lrr-2001-6 |doi-access=free |pmid=28163633 |pmc=5253844}}</ref>

The link with the laws of thermodynamics was further strengthened by Hawking's discovery in 1974 that quantum field theory predicts that a black hole radiates [[blackbody radiation]] at a constant temperature. This seemingly causes a violation of the second law of black hole mechanics, since the radiation will carry away energy from the black hole causing it to shrink. The radiation also carries away entropy, and it can be proven under general assumptions that the sum of the entropy of the matter surrounding a black hole and one quarter of the area of the horizon as measured in Planck units is in fact always increasing. This allows the formulation of the [[first law of black hole mechanics]] as an analogue of the [[first law of thermodynamics]], with the mass acting as energy, the surface gravity as temperature and the area as entropy.<ref name="wald99" />

One puzzling feature is that the entropy of a black hole scales with its area rather than with its volume, since entropy is normally an [[extensive quantity]] that scales linearly with the volume of the system. This odd property led [[Gerard 't Hooft]] and [[Leonard Susskind]] to propose the [[holographic principle]], which suggests that anything that happens in a volume of spacetime can be described by data on the boundary of that volume.<ref>{{cite book|last='t Hooft|first=G.|title=Basics and Highlights in Fundamental Physics|publisher=[[World Scientific Publishing]]|year=2001|isbn=978-981-02-4536-8|editor-last=Zichichi|editor-first=A.|series=Subnuclear series|volume=37|pages=72–100|chapter=The Holographic Principle|bibcode=2001bhfp.conf...72T|doi=10.1142/9789812811585_0005|arxiv=hep-th/0003004|s2cid=119383028}}</ref>

Although general relativity can be used to perform a semiclassical calculation of black hole entropy, this situation is theoretically unsatisfying. In [[statistical mechanics]], entropy is understood as counting the number of microscopic configurations of a system that have the same macroscopic qualities, such as mass, charge, pressure, etc. Without a satisfactory theory of quantum gravity, one cannot perform such a computation for black holes. Some progress has been made in various approaches to quantum gravity. In 1995, [[Andrew Strominger]] and [[Cumrun Vafa]] showed that counting the microstates of a specific supersymmetric black hole in string theory reproduced the Bekenstein–Hawking entropy.<ref>{{cite journal |last1=Strominger |first1=A. |last2=Vafa |first2=C. |title=Microscopic origin of the Bekenstein-Hawking entropy |journal=Physics Letters B |volume=379 |issue=1–4 |pages=99–104 |date=1996 |doi=10.1016/0370-2693(96)00345-0 |arxiv=hep-th/9601029 |bibcode=1996PhLB..379...99S |s2cid=1041890}}</ref> Since then, similar results have been reported for different black holes both in string theory and in other approaches to quantum gravity like [[loop quantum gravity]].<ref>{{Cite book |last1=Carlip |first1=S. |title=Physics of Black Holes |volume=769 |pages=89–123 |date=2009 |doi=10.1007/978-3-540-88460-6_3 |arxiv=0807.4520 |series=Lecture Notes in Physics |isbn=978-3-540-88459-0|bibcode=2009LNP...769...89C |chapter=Black Hole Thermodynamics and Statistical Mechanics|location=Berlin |publisher=Springer |s2cid=15877702 }}</ref>

=== Information loss paradox ===
{{Main|Black hole information paradox}}
{{unsolved|physics|Is physical information lost in black holes?}}

Because a black hole has only a few internal parameters, most of the information about the matter that went into forming the black hole is lost. Regardless of the type of matter which goes into a black hole, it appears that only information concerning the total mass, charge, and angular momentum are conserved. As long as black holes were thought to persist forever this information loss is not that problematic, as the information can be thought of as existing inside the black hole, inaccessible from the outside, but represented on the event horizon in accordance with the holographic principle. However, black holes slowly evaporate by emitting Hawking radiation. This radiation does not appear to carry any additional information about the matter that formed the black hole, meaning that this information appears to be gone forever.<ref name="PlayDice000">{{cite web |title=Does God Play Dice? |first=S. W. |last=Hawking |url=http://www.hawking.org.uk/does-god-play-dice.html |website=www.hawking.org.uk |access-date=14 March 2009 |archive-url=https://web.archive.org/web/20120111012413/http://www.hawking.org.uk/does-god-play-dice.html |archive-date=11 January 2012 }}</ref>

The question whether information is truly lost in black holes (the [[black hole information paradox]]) has divided the theoretical physics community. In quantum mechanics, loss of information corresponds to the violation of a property called [[unitarity (physics)|unitarity]], and it has been argued that loss of unitarity would also imply violation of conservation of energy,<ref name="giddings1995">{{cite conference |first=S. B. |last=Giddings |title=The black hole information paradox |arxiv=hep-th/9508151 |book-title=Particles, Strings and Cosmology |date=1995 |conference=Johns Hopkins Workshop on Current Problems in Particle Theory 19 and the PASCOS Interdisciplinary Symposium 5 |bibcode=1995hep.th....8151G}}</ref> though this has also been disputed.<ref name="unruh2017"/> Over recent years evidence has been building that indeed information and unitarity are preserved in a full quantum gravitational treatment of the problem.<ref>{{cite conference |first=S. D. |last=Mathur |title=The information paradox: conflicts and resolutions |journal=Pramana |date=2011 |volume=79 |issue=5 |pages=1059–1073 |conference=XXV International Symposium on Lepton Photon Interactions at High Energies |arxiv=1201.2079 |bibcode=2012Prama..79.1059M |doi=10.1007/s12043-012-0417-z}}</ref>

One attempt to resolve the black hole information paradox is known as [[black hole complementarity]]. In 2012, the "[[Firewall (physics)|firewall paradox]]" was introduced with the goal of demonstrating that black hole complementarity fails to solve the information paradox. According to [[quantum field theory in curved spacetime]], a [[Black-body radiation|single emission]] of Hawking radiation involves two mutually [[quantum entanglement|entangled]] particles. The outgoing particle escapes and is emitted as a quantum of Hawking radiation; the infalling particle is swallowed by the black hole. Assume a black hole formed a finite time in the past and will fully evaporate away in some finite time in the future. Then, it will emit only a finite amount of information encoded within its Hawking radiation. According to research by physicists like [[Don Page (physicist)|Don Page]]<ref>{{cite journal |last1=Page |first1=Don N. |title=Information in black hole radiation |journal=[[Phys. Rev. Lett.]] |date=1993 |volume=71 |issue=23 |pages=3743–3746 |doi=10.1103/PhysRevLett.71.3743 |pmid=10055062 |bibcode=1993PhRvL..71.3743P |arxiv=hep-th/9306083 |citeseerx=10.1.1.267.174|s2cid=9363821 }}</ref><ref>{{cite journal |last1=Page |first1=Don N. |title=Average entropy of a subsystem |journal=[[Phys. Rev. Lett.]] |date=1993 |volume=71 |issue=9 |pages=1291–1294 |doi=10.1103/PhysRevLett.71.1291 |pmid=10055503 |bibcode=1993PhRvL..71.1291P |arxiv=gr-qc/9305007 |citeseerx=10.1.1.339.7694|s2cid=17058654 }}</ref> and Leonard Susskind, there will eventually be a time by which an outgoing particle must be entangled with all the Hawking radiation the black hole has previously emitted.

This seemingly creates a paradox: a principle called "[[monogamy of entanglement]]" requires that, like any quantum system, the outgoing particle cannot be fully entangled with two other systems at the same time; yet here the outgoing particle appears to be entangled both with the infalling particle and, independently, with past Hawking radiation.<ref>{{cite journal |last1=Merali |first1=Zeeya |title=Astrophysics: Fire in the hole! |journal=Nature |date=3 April 2013 |volume=496 |issue=7443 |pages=20–23 |doi=10.1038/496020a |pmid=23552926 |bibcode=2013Natur.496...20M |doi-access=free}}</ref> In order to resolve this contradiction, physicists may eventually be forced to give up one of three time-tested principles: Einstein's equivalence principle, unitarity, or local quantum field theory. One possible solution, which violates the equivalence principle, is that a "firewall" destroys incoming particles at the event horizon.<ref>{{cite journal | last1 = Amheiri | first1 = Ahmed | last2 = Marolf | first2 = Donald | last3 = Polchinski | first3 = Joseph | last4 = Sully | first4 = James | title = Black holes: Complementarity or Firewalls? | journal = Journal of High Energy Physics | date = 2013 | volume = 2013 | issue = 2 | page = 62 | doi = 10.1007/JHEP02(2013)062| arxiv = 1207.3123 | bibcode = 2013JHEP...02..062A | s2cid = 55581818 }}</ref> In general, which—if any—of these assumptions should be abandoned remains a topic of debate.<ref name="unruh2017">{{cite journal|first1=William G. |last1=Unruh |first2=Robert M. |last2=Wald |author-link1=W. G. Unruh |author-link2=Robert Wald |title=Information loss |journal=[[Reports on Progress in Physics]] |year=2017 |volume=80 |issue=9 |page=092002 |doi=10.1088/1361-6633/aa778e |pmid=28585922 |arxiv=1703.02140 |bibcode=2017RPPh...80i2002U|s2cid=39957660 }}</ref>

== In science fiction ==
{{Main|Black holes in fiction}}

[[Christopher Nolan|Christopher Nolan's]] 2014 science fiction epic ''[[Interstellar (film)|Interstellar]]'' features a black hole known as Gargantua, which is the central object of a planetary system in a distant galaxy. Humanity accessed this system via a [[wormhole]] in the outer [[Solar System|solar system]], near [[Saturn]].

== See also ==
{{Portal|Astronomy|History of science|Mathematics|Physics|Stars}}
{{Div col|colwidth=18em}}
* [[Black brane]] or [[Black string]]
* [[Black Hole Initiative]]
* [[Black hole starship]]
* [[Black holes in fiction]]
* [[Blanet]]
* [[BTZ black hole]]
* [[Dark star (dark matter)]]
* [[Golden binary]]
* [[Hypothetical black hole (disambiguation)]]
* [[Kugelblitz (astrophysics)]]
* [[List of black holes]]
* [[List of nearest black holes]]
* [[Outline of black holes]]
* [[Planck star]]
* [[Sonic black hole]]
* [[Susskind-Hawking battle]]
* [[Timeline of black hole physics]]
* [[Virtual black hole]]
* [[White hole]]
{{Div col end}}

== Notes ==
{{reflist|group="Note"}}

== References ==
{{reflist}}

==Sources==
* {{cite book |last1=Carroll |first1=Sean M. | author-link = Sean M. Carroll |title=Spacetime and Geometry |date=2004 |publisher=Addison Wesley |isbn=978-0-8053-8732-2  }}, the lecture notes on which the book was based are available for free from Sean Carroll's [https://www.preposterousuniverse.com/spacetimeandgeometry/ website] {{Webarchive|url=https://web.archive.org/web/20170323013522/http://www.preposterousuniverse.com/spacetimeandgeometry/ |date=23 March 2017 }}
* {{cite book |last1=Hawking |first1=S. W. |last2=Ellis |first2=G. F. R. |author-link1=Stephen Hawking | author2-link = George F. R. Ellis |title=Large Scale Structure of space time |publisher=Cambridge University Press |date=1973 |url=https://books.google.com/books?id=QagG_KI7Ll8C |isbn=978-0-521-09906-6 |access-date=16 May 2020 |archive-date=21 July 2020 |archive-url=https://web.archive.org/web/20200721064932/https://books.google.com/books?id=QagG_KI7Ll8C |url-status=live }}
* {{cite book |last1=Misner |first1=Charles |last2=Thorne |first2=Kip S. |last3=Wheeler |first3=John |author1-link=Charles W. Misner |author2-link=Kip Thorne |author3-link=John Archibald Wheeler |title=Gravitation |publisher=W. H. Freeman and Company |date=1973 |isbn=978-0-7167-0344-0  }}
* {{Cite book |last1=Thorne |first1=Kip S. |author-link=Kip Thorne |title=Black Holes and Time Warps |publisher=Norton, W. W. & Company, Inc |date=1994 |isbn=978-0-393-31276-8|title-link=Black Holes and Time Warps  }}
* {{cite book |last=Wald |first=Robert M. |author-link=Robert Wald |title=General Relativity |publisher=University of Chicago Press |date=1984 |isbn=978-0-226-87033-5 |url=https://books.google.com/books?id=9S-hzg6-moYC |access-date=23 February 2016 |archive-date=11 August 2016 |archive-url=https://web.archive.org/web/20160811035125/https://books.google.com/books?id=9S-hzg6-moYC |url-status=live }}
* {{cite book |last=Wheeler |first=J. Craig | author-link = J. Craig Wheeler |title=Cosmic Catastrophes |edition=2nd |publisher=Cambridge University Press |date=2007 |isbn=978-0-521-85714-7  }}

== Further reading ==
=== Popular reading ===
{{refbegin}}
* {{Cite book |last1=Begelman |first1=Mitchell C. |url=https://books.google.com/books?id=ZPwAEAAAQBAJ |title=Gravity's fatal attraction: black holes in the universe |last2=Rees |first2=Martin J. |date=2021 |publisher=Cambridge University Press |isbn=978-1-108-87112-9 |edition=3rd |location=Cambridge, United Kingdom ; New York, NY}}
* {{cite book |last1=Ferguson |first1=Kitty |title=Black Holes in Space-Time |publisher=Watts Franklin |date=1991 |isbn=978-0-531-12524-3 |ref=none}}
* {{cite book |first1=Stephen |last1=Hawking |author1-link=Stephen Hawking |title=A Brief History of Time |publisher=Bantam Books, Inc |date=1988 |isbn=978-0-553-38016-3|title-link=A Brief History of Time  |ref=none}}
* {{cite book |first1=Stephen |last1=Hawking |author1-link=Stephen Hawking |first2=Roger |last2=Penrose |author2-link=Roger Penrose |title=The Nature of Space and Time |date=1996 |publisher=Princeton University Press |isbn=978-0-691-03791-2 |url=https://books.google.com/books?id=LstaQTXP65cC |ref=none |access-date=16 May 2020 |archive-date=18 October 2021 |archive-url=https://web.archive.org/web/20211018031528/https://books.google.com/books?id=LstaQTXP65cC |url-status=live }}
* {{cite book |last1=Levin |first1=Janna |title=Black hole survival guide |date=2020 |publisher=Alfred A. Knopf |location=New York |isbn=978-0-525-65822-1 |url=https://books.google.com/books?id=9rITEAAAQBAJ |access-date=6 November 2021 |archive-date=22 March 2022 |archive-url=https://web.archive.org/web/20220322141933/https://www.google.com/books/edition/Black_Hole_Survival_Guide/9rITEAAAQBAJ?hl=en&gbpv=1&dq=janna+levin&printsec=frontcover |url-status=live }}
* {{cite book |last1=Melia |first1=Fulvio |author1-link=Fulvio Melia |title=The Black Hole at the Center of Our Galaxy |publisher=Princeton U Press |date=2003 |isbn=978-0-691-09505-9 |url-access=registration |url=https://archive.org/details/blackholeatcente0000meli |ref=none }}
* {{cite book |last1=Melia |first1=Fulvio |title=The Edge of Infinity. Supermassive Black Holes in the Universe |publisher=Cambridge U Press |date=2003 |isbn=978-0-521-81405-8 |url-access=registration |url=https://archive.org/details/edgeofinfinitysu00meli |ref=none }}
* {{cite book |last1=Pickover |first1=Clifford |title=Black Holes: A Traveler's Guide |publisher=Wiley, John & Sons, Inc |date=1998 |isbn=978-0-471-19704-1 |ref=none}}
* {{Cite book |last=Susskind |first=Leonard |author-link=Leonard Susskind |title=The black hole war: my battle with Stephen Hawking to make the world safe for quantum mechanics |title-link=The Black Hole War |date=2008 |publisher=Little, Brown |isbn=978-0-316-01640-7 |edition=1st |location=New York |oclc=181603165 |ref=none}}
{{refend}}

=== University textbooks and monographs ===
{{refbegin}}
* {{Cite book |last=Carter |first=B. |author-link=Brandon Carter |title=Black holes |date=1973 |publisher=Gordon and Breach |isbn=978-0-677-15610-1 |editor-last=DeWitt-Morette |editor-first=Cécile |location=New York |chapter=Black hole equilibrium states |ref=none |editor-last2=DeWitt |editor-first2=Bryce S. |editor-link2=Bryce De Witt}}
* {{cite book |last1=Chandrasekhar |first1=Subrahmanyan |author-link1=Subrahmanyan Chandrasekhar |title=Mathematical Theory of Black Holes |publisher=Oxford University Press |date=1999 |isbn=978-0-19-850370-5  |ref=none}}
* {{cite book |doi=10.1007/978-94-011-5139-9 |title=Black Hole Physics |series=Fundamental Theories of Physics |year=1998 |volume=96 |isbn=978-0-7923-5146-7 |ref=none |last1=Frolov |first1=Valeri P. |last2=Novikov |first2=Igor D. }}
* {{cite book |last1=Frolov |first1=Valeri P. |last2=Zelnikov |first2=Andrei |title=Introduction to Black Hole Physics |publisher=Oxford University Press |date=2011 |location=Oxford |url=https://books.google.com/books?id=r_l5AK9DdXsC&pg=PA34 |isbn=978-0-19-969229-3 |zbl=1234.83001 |ref=none |access-date=2 January 2022 |archive-date=22 March 2022 |archive-url=https://web.archive.org/web/20220322142008/https://books.google.com/books?id=r_l5AK9DdXsC&pg=PA34 |url-status=live }}
* {{cite book |last1=Melia |first1=Fulvio |author1-link=Fulvio Melia |title=The Galactic Supermassive Black Hole |publisher=Princeton U Press |date=2007 |isbn=978-0-691-13129-0  |ref=none}}
* {{cite book |last1=Taylor |first1=Edwin F. |last2=Wheeler |first2=John Archibald |author2-link=John Archibald Wheeler |title=Exploring Black Holes |publisher=Addison Wesley Longman |date=2000 |isbn=978-0-201-38423-9  |ref=none}}
* {{cite book |last1=Wald |first1=Robert M. |title=Space, Time, and Gravity: The Theory of the Big Bang and Black Holes |publisher=University of Chicago Press |date=1992 |isbn=978-0-226-87029-8  |ref=none}}
* {{cite journal |doi=10.4249/scholarpedia.4277|bibcode=2008SchpJ...3.4277C|title=Black holes|year=2008|last1=Price|first1=Richard|last2=Creighton|first2=Teviet|journal=Scholarpedia|volume=3|issue=1|page=4277|doi-access=free  |ref=none}}
{{refend}}

=== Review papers ===
{{refbegin}}
* {{cite arXiv |eprint=hep-ph/0511217 |last1=Hughes |first1=Scott A. |title=Trust but verify: The case for astrophysical black holes |date=2005  |ref=none}} Lecture notes from 2005 [[SLAC]] Summer Institute.
* {{cite journal |last1=Gallo |first1=Elena |last2=Marolf |first2=Donald |doi=10.1119/1.3056569 |title=Resource Letter BH-2: Black Holes |date=2009 |issue=4 |pages=294–307 |volume=77 |journal=American Journal of Physics |arxiv=0806.2316 |bibcode=2009AmJPh..77..294G |s2cid=118494056}}
* {{cite journal |last1=Cardoso |first1=Vitor |last2=Pani |first2=Paolo |title=Testing the nature of dark compact objects: a status report |journal=Living Reviews in Relativity |volume=22 |issue=1 |page=4 |year=2019 |doi=10.1007/s41114-019-0020-4 |arxiv=1904.05363 |bibcode=2019LRR....22....4C |s2cid=256465740}}
* {{cite journal |last1=Mann |first1=Robert B. |last2=Murk |first2=Sebastian |last3=Terno |first3=Daniel R. |title=Black holes and their horizons in semiclassical and modified theories of gravity |journal=International Journal of Modern Physics D |volume=31 |issue=9 |pages=2230015–2230276 |year=2022 |doi=10.1142/S0218271822300154 |arxiv=2112.06515 |bibcode=2022IJMPD..3130015M |s2cid=245123647}}
{{refend}}

== External links ==
<!--Please do not add any more external links here. Wikipedia is not a collection of links. For details, please see [[Wikipedia:External links]] and [[WP:LINKFARM-->
{{Sister project links|d=Q589|voy=no|wikt=black hole|c=Category:Black holes|n=Category:Black holes|s=no|b=General Astronomy/Black holes/Introduction}}
{{Scholia}}
* {{In Our Time|Black Holes|p00547f4|Black_Holes}}
* ''[[Stanford Encyclopedia of Philosophy]]'': "[https://plato.stanford.edu/entries/spacetime-singularities/ Singularities and Black Holes]" by Erik Curiel and Peter Bokulich.
* [https://hubblesite.org/contents/articles/black-holes.html Black Holes: Gravity's Relentless Pull] – Interactive multimedia Web site about the physics and astronomy of black holes from the Space Telescope Science Institute (HubbleSite)
* [[ESA]]'s [https://www.esa.int/gsp/ACT/phy/Projects/Blackholes/WebGL.html Black Hole Visualization] {{Webarchive|url=https://web.archive.org/web/20190503070935/https://www.esa.int/gsp/ACT/phy/Projects/Blackholes/WebGL.html |date=3 May 2019 }}
* [https://apod.nasa.gov/htmltest/gifcity/bh_pub_faq.html Frequently Asked Questions (FAQs) on Black Holes]
* [https://web.archive.org/web/19980118051503/http://casa.colorado.edu/~ajsh/schwp.html Schwarzschild Geometry]
* [https://www.nytimes.com/2021/04/22/science/black-holes-astrophysics-names.html Black holes - basic (NYT; April 2021)]

=== Videos ===
* [https://www.eso.org/public/videos/eso0846b/ 16-year-long study tracks stars orbiting Sagittarius A*]
* [https://web.archive.org/web/20040925044354/http://www.mpe.mpg.de/ir/GC/index.php Movie of Black Hole Candidate from Max Planck Institute]
* {{cite journal |last1=Cowen |first1=Ron |title=3D simulations of colliding black holes hailed as most realistic yet |journal=Nature |date=20 April 2015 |doi=10.1038/nature.2015.17360 |doi-access=free |ref=none}}
* [https://www.bbc.com/news/science-environment-35524440 Computer visualisation of the signal detected by LIGO]
* [https://www.youtube.com/watch?v=I_88S8DWbcU Two Black Holes Merge into One (based upon the signal GW150914)]

{{Black holes}}
{{Relativity}}
{{String theory topics}}
{{Authority control}}

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