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[[File:BH LMC.png|thumb|upright=1.35|right|Simulated view of a black hole (center) in front of the [[Large Magellanic Cloud]]. Note the [[gravitational lens]]ing effect, which produces two enlarged but highly distorted views of the Cloud. Across the top, the [[Milky Way]] disk appears distorted into an arc.]]
{{General relativity|cTopic=Phenomena}}


A '''black hole''' is a region of [[spacetime]] from which gravity prevents anything, including [[light]], from escaping.<ref>{{harvnb|Wald|1984|pp=299–300}}</ref>  The theory of [[general relativity]] predicts that a sufficiently compact [[mass]] will deform spacetime to form a black hole. Around a black hole, there is a mathematically defined surface called an [[event horizon]] that marks the [[point of no return]]. The hole is called "black" because it absorbs all the light that hits the horizon, reflecting nothing, just like a perfect [[black body]] in [[thermodynamics]].<ref>{{cite book
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|title=Gravity from the ground up
|edition=
|first1=Bernard F. |last1=Schutz |authorlink1=Bernard F. Schutz
|publisher=Cambridge University Press
|year=2003
|isbn=0-521-45506-5
|page=110
|url=http://books.google.com/books?id=P_T0xxhDcsIC}}</ref><ref>{{Cite journal
|last=Davies |first=P. C. W. |authorlink1=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 |year = 1978
|issue=8 |pages = 1313–1355
|doi = 10.1088/0034-4885/41/8/004
|bibcode = 1978RPPh...41.1313D
|ref=harv }}</ref> [[Quantum field theory in curved spacetime]] predicts that event horizons emit [[Hawking radiation|radiation]] like a black body with a finite [[temperature]]. This temperature is inversely proportional to the mass of the black hole, making it difficult to observe this radiation for [[stellar black hole|black holes of stellar mass]] or greater.
 
Objects whose [[gravity field]]s are too strong for light to escape were first considered in the 18th century by [[John Michell]] and [[Pierre-Simon Laplace]]. The first modern solution of general relativity that would characterize a black hole was found by [[Karl Schwarzschild]] in 1916, although its interpretation as a region of space from which nothing can escape was first published by [[David Finkelstein]] in 1958. Long considered a mathematical curiosity, it was during the 1960s that theoretical work showed black holes were a generic prediction of general relativity. The discovery of [[neutron star]]s sparked interest in [[gravitational collapse|gravitationally collapsed]] compact objects as a possible astrophysical reality.
 
[[Stellar black hole|Black holes of stellar mass]] are expected to form when very massive stars collapse at the end of their life cycle. After a black hole has formed it can continue to grow by absorbing mass from its surroundings. By absorbing other stars and merging with other black holes, [[supermassive black hole]]s of millions of solar masses may form. There is general consensus that supermassive black holes exist in the centers of most [[galaxy|galaxies]].
 
Despite its invisible interior, the presence of a black hole can be inferred through its interaction with other [[matter]] and with [[electromagnetic radiation]] such as light. Matter falling onto a black hole can form an [[accretion disk]] heated by friction, forming some of the [[Quasar|brightest objects in the universe]]. If there are other stars orbiting a black hole, their orbit can be used to determine its mass and location. These data can be used to exclude possible alternatives (such as neutron stars). In this way, astronomers have identified numerous stellar black hole candidates in [[binary star|binary systems]], and established that the core of our [[Milky Way]] galaxy contains a supermassive black hole of about 4.3 million [[solar mass]]es.
 
{{TOC limit}}
 
==History==
[[File:Black hole lensing web.gif|right|frame|alt=Schwarzschild black hole|Simulation of [[gravitational lens]]ing by a black hole, which distorts the image of a [[galaxy]] in the background ([[:File:BlackHole Lensing.gif|larger animation]])]]
The idea of a body so massive that even light could not escape was first put forward by [[John Michell]] in a letter written to [[Henry Cavendish]] in 1783 of the [[Royal Society]]:
 
{{quote|If the semi-diameter of a sphere of the same density as the Sun were to exceed that of the Sun in the proportion of 500 to 1, a body falling from an infinite height towards it would have acquired at its surface greater velocity than that of light, and consequently supposing light to be attracted by the same force in proportion to its vis inertiae, with other bodies, all light emitted from such a body would be made to return towards it by its own proper gravity.|John Michell<ref name="Michell1784">
{{Cite journal
|last=Michell |first=J. |authorlink1=John Michell
|year=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
|issue=0 |pages=35–57
|bibcode=1784RSPT...74...35M
|doi=10.1098/rstl.1784.0008
|ref=harv
|jstor=106576
}}</ref>}} In 1796, mathematician [[Pierre-Simon Laplace]] promoted the same idea in the first and second editions of his book ''Exposition du système du Monde'' (it was removed from later editions).<ref>{{cite book
| first=C. C. | last=Gillispie
| year=2000
| title=Pierre-Simon Laplace, 1749–1827: a life in exact science
| series=Princeton paperbacks | page=175
| publisher=Princeton University Press | isbn=0-691-05027-9
| url=http://books.google.com/books?id=iohJomX0IWgC&pg=PA175 }}</ref><ref>
{{cite book
|last=Israel |first=W.
|chapter=Dark stars: the evolution of an idea
|url=http://books.google.com/books?id=Vq787qC5PWQC&lpg=PP1&pg=PA199#v=onepage&q&f=false
|editor1-last=Hawking |editor1-first=S. W. |editor1-link=Stephen Hawking
|editor2-last=Israel |editor2-first=W.
|year=1989
|title=300 Years of Gravitation
|publisher=[[Cambridge University Press]]
|isbn=978-0-521-37976-2
}}</ref> Such "[[dark star (Newtonian mechanics)|dark star]]s" were largely ignored in the nineteenth century, since it was not understood how a massless wave such as light could be influenced by gravity.<ref>{{harvnb|Thorne|1994|pp=123–124}}</ref>
 
===General relativity===
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]], which describes the [[gravitational field]] of a [[point mass]] and a spherical mass.<ref name="Schwarzschild1916">
{{Cite journal
|last=Schwarzschild |first=K. |authorlink1=Karl Schwarzschild
|year=1916
|title=Über das Gravitationsfeld eines Massenpunktes nach der Einsteinschen Theorie
|url=http://www.archive.org/stream/sitzungsberichte1916deutsch#page/188/mode/2up
|journal=[[Sitzungsberichte der Königlich Preussischen Akademie der Wissenschaften]]
|volume=7 |pages=189–196
|ref=harv
}} and {{Cite journal
|last=Schwarzschild |first=K. |authorlink1=Karl Schwarzschild
|year=1916
|title=Über das Gravitationsfeld eines Kugel aus inkompressibler Flüssigkeit nach der Einsteinschen Theorie
|url=http://www.archive.org/stream/sitzungsberichte1916deutsch#page/424/mode/2up
|journal=[[Sitzungsberichte der Königlich Preussischen Akademie der Wissenschaften]]
|volume=18 |pages=424–434
|ref=harv
}}</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
|year=1917 |volume=19 |issue=1 |pages=197–215
|url=http://www.dwc.knaw.nl/DL/publications/PU00012325.pdf
|ref=harv
}}</ref><ref>{{cite book
|title=Studies in the history of general relativity
|editor1-last=Eisenstaedt |editor1-first=J.
|editor2-last=Kox |editor2-first=A. J.
|isbn=978-0-8176-3479-7
|year=1992
|publisher=Birkhäuser
|chapter=General Relativity in the Netherlands: 1915–1920
|last=Kox |first=A. J.
|chapter-url=http://books.google.nl/books?id=vDHCF_3vIhUC&pg=PA41
|page=41
}}{{dead link|date=February 2013}}<!--On first try, substitutes page 41 with "U bent bij een pagina gekomen die geen deel uitmaakt van het voorbeeld, of u heeft uw weergavelimiet voor dit boek bereikt." = "You have reached a page that is not part of the sample, or reached your viewing limit for this book." --></ref> This solution had a peculiar behaviour at what is now called the [[Schwarzschild radius]], where it became [[mathematical singularity|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 (see [[Eddington–Finkelstein coordinates]]), although it took until 1933 for [[Georges Lemaître]] to realize that this meant the singularity at the Schwarzschild radius was an unphysical [[coordinate singularity]].<ref name="HooftHist">{{Cite journal
|last='t Hooft |first=G. |authorlink1=Gerard 't Hooft
|year=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
|ref=harv
}}</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 1.4 solar masses) has no stable solutions.<ref name=venkataraman92>{{cite book
| first=G. | last=Venkataraman
| title=Chandrasekhar and his limit
| page=89 | publisher=Universities Press
| year=1992 | url=http://books.google.com/books?id=HNSdDFOJ4wkC&pg=PA89
| isbn=81-7371-035-X
}}</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.
|year=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
|ref=harv
|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.
|year=1994
|title=Stellar evolution
|url=http://books.google.com/books?id=kd4VEZv8oo0C&pg=PA105
|publisher=[[A K Peters, Ltd.|A K Peters]]
|page=105
|isbn=1-56881-012-1
}}</ref> which is itself stable because of the [[Pauli exclusion principle]]. But in 1939, [[Robert Oppenheimer]] and others predicted that neutron stars above approximately three solar masses (the [[Tolman–Oppenheimer–Volkoff limit]]) would collapse into black holes 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
|last= Oppenheimer |first=J. R. |authorlink1=J. Robert Oppenheimer
|last2=Volkoff |first2=G. M. |authorlink2=George Volkoff
|year = 1939
|title = On Massive Neutron Cores
|journal = [[Physical Review]]
|volume = 55 |issue = 4 |pages = 374–381
|doi = 10.1103/PhysRev.55.374
|ref = harv
|bibcode = 1939PhRv...55..374O }}</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. Because of this property, the collapsed stars were called "frozen stars",<ref>
{{Cite journal
|last=Ruffini |first=R. |authorlink1=Remo Ruffini
|last2=Wheeler |first2=J. A. |authorlink2=John Archibald Wheeler
|year=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
|ref=harv
}}</ref> because an outside observer would see the surface of the star frozen in time at the instant where its collapse takes it inside the Schwarzschild radius.
 
===Golden age===
{{See also|Golden age of general relativity}}
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. |authorlink1=David Finkelstein
|year=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
|ref=harv
|bibcode = 1958PhRv..110..965F }}</ref> This did not strictly contradict Oppenheimer's results, but extended them to include the point of view of infalling observers. [[Eddington-Finkelstein coordinates|Finkelstein's solution]] extended the Schwarzschild solution for the future of observers falling into a black hole. A [[Kruskal-Szekeres coordinates|complete extension]] had already been found by [[Martin Kruskal]], who was urged to publish it.<ref>
{{cite journal
|last1=Kruskal |first1=M. |authorlink1=Martin Kruskal
|year=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=harv }}</ref>
 
These results came at the beginning of the [[golden age of general relativity]], which was marked by general relativity and black holes becoming mainstream subjects of research. This process was helped by the discovery of [[pulsar]]s in 1967,<ref>
{{Cite journal
| display-authors=1 | last1=Hewish | first1=A. |authorlink1=Antony Hewish
| last2=Bell | first2=S. J. |authorlink2=Jocelyn Bell Burnell
| last3=Pilkington | first3=J. D. H.
| last4=Scott | first4=P. F. | last5=Collins | first5=R. A.
|year=1968
|title=Observation of a Rapidly Pulsating Radio Source
|journal=[[Nature (journal)|Nature]]
|volume=217
|issue=5130 |pages=709–713
|doi=10.1038/217709a0
|ref=harv
|bibcode=1968Natur.217..709H
| postscript=<!-- Bot inserted parameter. Either remove it; or change its value to "." for the cite to end in a ".", as necessary. -->{{inconsistent citations}}
}}</ref><ref>
{{Cite journal
| display-authors=1 | last1=Pilkington | first1=J. D. H.
| last2=Hewish | first2=A. |authorlink2=Antony Hewish
| last3=Bell | first3=S. J. |authorlink3=Jocelyn Bell Burnell
| last4=Cole | first4=T. W.
|year=1968
|title=Observations of some further Pulsed Radio Sources
|journal=[[Nature (journal)|Nature]]
|volume=218
|issue=5137 |pages=126–129
|doi=10.1038/218126a0
|ref=harv
|bibcode = 1968Natur.218..126P
| postscript=<!-- Bot inserted parameter. Either remove it; or change its value to "." for the cite to end in a ".", as necessary. -->{{inconsistent citations}} }}</ref> which, by 1969, were shown to be rapidly rotating [[neutron star]]s.<ref name="araa8_265">
{{cite journal
| last=Hewish | first=A. |authorlink1=Antony Hewish
| year=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=harv
}}</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.
 
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 [[electric charge|electrically charged]].<ref>
{{Cite journal
| display-authors=1 | last1=Newman | first1=E. T. |authorlink1=Ezra T. Newman
| last2=Couch | first2=E. | last3=Chinnapared | first3=K.
| last4=Exton | first4=A. | last5=Prakash | first5=A.
| last6=Torrence | first6=R.
|year=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=harv
| postscript=<!-- Bot inserted parameter. Either remove it; or change its value to "." for the cite to end in a ".", as necessary. -->{{inconsistent citations}} }}</ref> Through the work of [[Werner Israel]],<ref>
{{cite journal
|last=Israel |first=W.
|year=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=harv }}</ref> [[Brandon Carter]],<ref>
{{cite journal
|last=Carter |first=B. |authorlink1=Brandon Carter
|year=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=harv
}}</ref><ref>
{{cite book
|last=Carter |first=B. |authorlink1=Brandon Carter
|year=1977
|chapter=The vacuum black hole uniqueness theorem and its conceivable generalisations
|editor-last= |editor-first=
|title=Proceedings of the 1st Marcel Grossmann meeting on general relativity
|pages=243–254
|publisher=
|isbn=
}}</ref> and David Robinson<ref>
{{cite journal
|last1=Robinson |first1=D.
|year=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=harv
}}</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 artifacts 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. |authorlink1=Roger Penrose
|year=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
|ref=harv
}}</ref> and [[Stephen Hawking]] used global techniques to prove that singularities appear generically.<ref>
{{cite journal
|last1=Ford |first1=L. H.
|year=2003
|title=The Classical Singularity Theorems and Their Quantum Loopholes
|journal=[[International Journal of Theoretical Physics]]
|volume=42
|issue=6 |page=1219
|doi=10.1023/A:1025754515197
|ref=harv
}}</ref>
 
Work by [[James M. Bardeen|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. |authorlink1=James M. Bardeen
|last2=Carter |first2=B. |authorlink2=Brandon Carter
|last3=Hawking |first3=S. W. |authorlink3=Stephen Hawking
|year=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=MR0334798
|zbl=1125.83309
|ref=harv
|bibcode = 1973CMaPh..31..161B }}</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]] predicts that black holes should radiate like a [[black body]] with a temperature proportional to the [[surface gravity]] of the black hole.<ref name=Hawking1974/>
 
The first use of the term "black hole" in print was by 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]].<ref>
{{cite web
|last=Quinion |first=M. |authorlink1=Michael Quinion
|date=26 April 2008
|title=Black Hole
|work=[[World Wide Words]]
|url=http://www.worldwidewords.org/topicalwords/tw-bla1.htm
|accessdate=2008-06-17
}}</ref> [[John Archibald Wheeler|John Wheeler]] used term "black hole" a lecture in 1967, leading some to credit him with coining the phrase. After Wheeler's use of the term, it was quickly adopted in general use.
 
==Properties and structure==
The [[no-hair theorem]] states that, once it achieves a stable condition after formation, a black hole has only three independent physical properties: [[mass]], [[electric charge|charge]], and [[angular momentum]].<ref name="HeuslerNoHair">{{Cite journal
|last=Heusler |first=M.
|year=1998
|title=Stationary Black Holes: Uniqueness and Beyond
|journal=Living Reviews in Relativity
|volume=1 |issue=6
|url= http://relativity.livingreviews.org/Articles/lrr-1998-6/
|archiveurl=http://web.archive.org/web/19990203021646/http://www.livingreviews.org/Articles/Volume1/1998-6heusler/
|archivedate=1999-02-03
|accessdate=2011-02-08
|ref=harv
|doi=10.12942/lrr-1998-6}}</ref> Any two black holes that share the same values for these properties, or parameters, are indistinguishable according to [[classical mechanics|classical]] (i.e. non-[[quantum mechanics|quantum]]) mechanics.
 
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 analog of [[Gauss's law]], the [[ADM mass]], far away from the black hole.<ref>{{harvnb|Carroll|2004|p=253}}</ref> Likewise, the angular momentum can be measured from far away using [[frame dragging]] by the [[gravitomagnetism|gravitomagnetic field]].
 
When an object falls into a black hole, any [[physical information|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 behavior 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. |authorlink1=Kip Thorne
|last2=Price |first2=R. H. |authorlink2=Richard H. Price
|publisher=Yale University Press
|year=1986
|isbn=978-0-300-03770-8}}</ref> This is different from other [[field theory (physics)|field theories]] like electromagnetism, which do not have any friction or resistivity at the microscopic level, because they are [[T-symmetry|time-reversible]]. 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 behavior is so puzzling that it has been called the [[black hole information loss paradox]].<ref>{{cite web
|url=http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/info_loss.html
|title=The Black Hole Information Loss Problem
|work=Usenet Physics FAQ
|last=Anderson|first=Warren G.
|year=1996
|accessdate=2009-03-24}}</ref><ref>{{cite conference
|last=Preskill |first=J. |authorlink1=John Preskill
|url=http://www.theory.caltech.edu/~preskill/talks/blackholes.pdf
|title=Black holes and information: A crisis in quantum physics
|date=1994-10-21
|conference=Caltech Theory Seminar}}</ref>
 
===Physical properties===
The simplest static black holes have mass but neither electric charge nor angular momentum. These black holes are often referred to as [[Schwarzschild metric|Schwarzschild black hole]]s 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 that there is no observable difference 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 only correct 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 | year=2007 | isbn=0-495-11352-2
| url=http://books.google.com/books?id=CXom04KGIL8C&pg=PA167
| ref=harv
| postscript=<!-- Bot inserted parameter. Either remove it; or change its value to "." for the cite to end in a ".", as necessary. -->{{inconsistent citations}} }}</ref>
 
Solutions describing more general black holes also exist. [[Charged black hole]]s are described by the [[Reissner–Nordström metric]], while the [[Kerr metric]] describes a [[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 | year=1983
| isbn=0-471-87316-0 }}</ref>
 
While the mass of a black hole can take any positive value, the charge and angular momentum are constrained by the mass. In [[Planck units]], the total electric charge&nbsp;''Q'' and the total angular momentum&nbsp;''J'' are expected to satisfy
:<math>Q^2+\left ( \tfrac{J}{M} \right )^2\le M^2\, </math>
for a black hole of mass ''M''. Black holes saturating 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>{{cite arXiv
|last=Wald
|first=R. M.
|author-link=Robert Wald
|title=Gravitational Collapse and Cosmic Censorship
|year=1997
|eprint=gr-qc/9710068
|class=gr-qc
}}</ref> This is supported by numerical simulations.<ref>{{Cite journal
|last=Berger|first=B. K.
|year=2002
|url=http://www.livingreviews.org/lrr-2002-1
|title=Numerical Approaches to Spacetime Singularities
|journal=Living Reviews in Relativity
|volume=5
|accessdate=2007-08-04
|ref=harv
|bibcode=2002LRR.....5....1B
|pages=1
|doi=10.12942/lrr-2002-1}}</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 common feature of compact 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 |year=2006 |pages=518–539
|arxiv=astro-ph/0606076
|doi=10.1086/508457 |ref=harv |bibcode=2006ApJ...652..518M}}</ref> appears to have an angular momentum near the maximum allowed value.
 
{| class="wikitable" style="float:right; margin:0 0 0.5em 1em;"
|+ Black hole classifications
|-
! Class !! Mass !! Size
|-
| [[Supermassive black hole]] || style="text-align: center;"| ~10<sup>5</sup>–10<sup>10</sup> [[solar mass|''M''<sub>Sun</sub>]] || style="text-align: center;"| ~0.001–400 [[Astronomical unit|AU]]
|-
| [[Intermediate-mass black hole]] || style="text-align: center;"| ~10<sup>3</sup> ''M''<sub>Sun</sub> || style="text-align: center;"| ~10<sup>3</sup> km ≈ [[Earth radius|''R''<sub>Earth</sub>]]
|-
| [[Stellar black hole]] || style="text-align: center;"| ~10 ''M''<sub>Sun</sub> || style="text-align: center;"| ~30&nbsp;km
|-
| [[Micro black hole]] || style="text-align: center;"| up to ~''M''<sub>[[Moon]]</sub> || style="text-align: center;"|up to ~0.1&nbsp;mm
|}
Black holes are commonly classified according to their mass, independent of angular momentum ''J'' or electric charge ''Q''. The size of a black hole, as determined by the radius of the event horizon, or [[Schwarzschild radius]], is roughly proportional to the mass ''M'' through
:<math>r_\mathrm{sh} =\frac{2GM}{c^2} \approx 2.95\, \frac{M}{M_\mathrm{Sun}}~\mathrm{km,}</math>
where ''r''<sub>sh</sub> is the Schwarzschild radius and ''M<sub>Sun</sub>'' is the [[solar mass|mass of the Sun]].<ref>{{harvnb|Wald|1984|pp=124–125}}</ref> This relation is exact only for black holes with zero charge and angular momentum; for more general black holes it can differ up to a factor of 2.
 
===Event horizon===
{{Main|Event horizon}}
{| class="wikitable" style="float:right; margin:0 0 1em 1em; width:400px; font-size:85%;"
|- width
| [[File:BH-no-escape-1.svg]]<br/>Far away from the black hole, a particle can move in any direction, as illustrated by the set of arrows. It is only restricted by the speed of light.
|-
| [[File:BH-no-escape-2.svg]]<br/>Closer to the black hole, spacetime starts to deform.  There are more paths going towards the black hole than paths moving away.{{#tag:ref|The set of possible paths, or more accurately the future [[light cone]] containing all possible [[world line]]s (in this diagram represented by the yellow/blue grid), 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 simply narrow without tilting as one approaches the event horizon, and in [[Kruskal–Szekeres coordinates]] the light cones don't change shape or orientation at all.<ref>{{harvnb|Thorne|Misner|Wheeler|1973|p=848}}</ref>|group="Note"}}
|-
| [[File:BH-no-escape-3.svg]]<br/>Inside of the event horizon, all paths bring the particle closer to the center 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 only pass inward towards the mass of the black hole. Nothing, not even light, can escape from inside the event horizon. 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 if 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 lead away from the black hole.
 
To a distant observer, clocks near a black hole appear to tick more slowly than those further away from the black hole.<ref>{{harvnb|Carroll|2004|p=217}}</ref> Due to this effect, known as [[gravitational time dilation]], an object falling into a black hole appears to slow down as it approaches the event horizon, taking an infinite time to reach it.<ref>{{harvnb|Carroll|2004|p=218}}</ref> At the same time, all processes on this object slow down, for a fixed outside observer, causing emitted light 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
|work=Knowing the universe and its secrets
|accessdate=2009-03-26}}</ref> Eventually, at a point just before it reaches the event horizon, the falling object becomes so dim that it can no longer be seen.
 
On the other hand, an observer falling into a black hole does not notice any of these effects as he crosses the event horizon. According to his own clock, he crosses the event horizon after a finite time without noting any singular behaviour. In particular, he is unable to determine exactly when he crosses it, as it is impossible to determine the location of the event horizon from local observations.<ref>{{harvnb|Carroll|2004|p=222}}</ref>
 
The shape of the event horizon of a black hole is always approximately spherical.{{#tag:ref|This is true only for 4-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 |year=2008
|url=http://relativity.livingreviews.org/Articles/lrr-2008-6/
|accessdate=2011-02-10
|arxiv=0801.3471
|bibcode = 2008LRR....11....6E |doi = 10.12942/lrr-2008-6
|ref=harv }}</ref><ref>{{cite journal
|last1=Obers |first1=N. A.
|editor1-last=Papantonopoulos
|editor1-first=Eleftherios
|title=Black Holes in Higher-Dimensional Gravity
|journal=Lecture Notes in Physics
|volume=769 |pages=211–258 |year=2009
|doi=10.1007/978-3-540-88460-6
|arxiv=0802.0519
|series=Lecture Notes in Physics
|isbn=978-3-540-88459-0
|ref=harv
}}</ref>|group="Note"}}<ref>{{harvnb|hawking|ellis|1973|loc=Ch. 9.3}}</ref> For non-rotating (static) black holes the geometry is precisely spherical, while for rotating black holes the sphere is somewhat oblate.
 
===Singularity===
{{Main|Gravitational singularity}}
At the center of a black hole as described by general relativity lies a [[gravitational singularity]], a region where the spacetime curvature becomes infinite.<ref>{{harvnb|Carroll|2004|p=205}}</ref> For a non-rotating black hole, this region takes the shape of a single point and for a [[rotating black hole]], it is smeared out to form a [[ring singularity]] lying 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]].
 
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 point; after attaining a certain ideal velocity, it is best to [[free fall]] the rest of the way.<ref>{{Cite journal
|last=Lewis |first=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 |year=2007
|doi=10.1071/AS07012
|arxiv=0705.1029
|bibcode = 2007PASA...24...46L
|ref=harv }}</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>
 
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 traveling to another universe is however only theoretical, since any perturbation will 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 |year=1996
|url=http://physicsworldarchive.iop.org/index.cfm?action=summary&doc=9%2F1%2Fphwv9i1a26%40pwa-xml&qt=%28Black%20holes\%3A%20the%20inside%20story%20%3Cin%3E%20%28chtitle%29%29
|ref=harv
|bibcode = 1996PhyW....9...34D
}}</ref> It also appears to be possible to follow [[closed timelike curve]]s (going back to one's own past) around the Kerr singularity, which lead 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| page=1796 |year=1990
|doi=10.1103/PhysRevD.41.1796
|bibcode = 1990PhRvD..41.1796P
|ref=harv }}</ref>
 
The appearance of singularities in general relativity is commonly perceived as signaling the breakdown of the theory.<ref>{{harvnb|Wald|1984|p=212}}</ref> This breakdown, however, is expected; it occurs in a situation 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 any singularities.<ref>{{cite web
|url=http://www.damtp.cam.ac.uk/user/gr/public/bh_hawk.html
|title=Black Holes and Quantum Gravity
|work=Cambridge Relativity and Cosmology
|last=Hamade |first=R.
|year=1996
|publisher=University of Cambridge
|accessdate=2009-03-26
}}</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
|accessdate=2009-03-26
}}</ref>
 
===Photon sphere===
{{Main|Photon sphere}}
The photon sphere is a spherical boundary of zero thickness such that [[photon]]s moving along [[tangent]]s to the sphere will be trapped in a circular orbit. For non-rotating black holes, the photon sphere has a radius 1.5 times the Schwarzschild radius. The orbits are [[instability|dynamically unstable]], hence any small perturbation (such as a particle of infalling matter) will grow over time, either setting it on an outward trajectory escaping the black hole or on an inward spiral eventually crossing 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
|date=September 2011
| doi=10.1103/PhysRevD.84.063008
| bibcode=2011PhRvD..84f3008N | arxiv=1106.242
| ref=harv
| postscript=<!-- Bot inserted parameter. Either remove it; or change its value to "." for the cite to end in a ".", as necessary. -->{{inconsistent citations}} }}</ref>
 
While light can still escape from inside the photon sphere, any light that crosses the photon sphere on an inbound trajectory will be captured by the black hole. Hence any light reaching an outside observer from inside the photon sphere must have been emitted by objects inside the photon sphere but still outside of the event horizon.<ref name=prd84_6/>
 
Other [[compact object]]s, such as [[neutron stars]], can also have photon spheres.<ref>{{Cite journal
|first=R. J. |last=Nemiroff
|title=Visual distortions near a neutron star and black hole
|journal= American Journal of Physics
|volume=61
|issue=7 |page=619 |year=1993
|doi=10.1119/1.17224
|arxiv=astro-ph/9312003
|ref=harv
|bibcode = 1993AmJPh..61..619N }}</ref> This follows from the fact that the gravitational field of an object does not depend on its actual size, hence any object that is smaller than 1.5 times the Schwarzschild radius corresponding to its mass will indeed have a photon sphere.
 
===Ergosphere===
{{Main|Ergosphere}}
[[File:Ergosphere.svg|thumb|right|ergosphere of a rotating black hole|The ergosphere is an oblate spheroid region outside of the event horizon, where objects cannot remain stationary.]]
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 becomes 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 bounded by the (outer) event horizon on the inside and an [[oblate spheroid]], which coincides with the event horizon at the poles and is noticeably wider around the equator. The outer boundary is sometimes called the ''ergosurface''.
 
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. This energy is taken from the rotational energy of the black hole causing it to slow down.<ref>{{harvnb|Carroll|2004|loc=Ch. 6.7}}</ref>
 
==Formation and evolution==
Considering the exotic nature of black holes, it may be natural to question if such bizarre objects could exist in nature or to suggest that they are merely pathological solutions to Einstein's equations. Einstein himself wrongly thought that black holes would not form, because he held that the angular momentum of collapsing particles would stabilize 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 |year=1939
|doi= 10.2307/1968902
|ref= harv
}}</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
|year=2009
|isbn=978-0-521-88512-6
|arxiv=0706.1109
}}</ref> and by the end of the 1960s, they had persuaded the majority of researchers in the field that there is no obstacle to forming an event horizon.
 
Once an event horizon forms, Penrose proved that a singularity will form somewhere inside it.<ref name=penrose1965/> Shortly afterwards, Hawking showed that many cosmological solutions describing the [[Big Bang]] have singularities without scalar fields or other exotic matter (see [[Penrose-Hawking singularity theorems]]). 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
|first=S. W. |last=Hawking |authorlink1=Stephen Hawking
|first2=R. |last2=Penrose |authorlink2=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
|ref=harv
|jstor=2416467
|bibcode = 1970RSPSA.314..529H }}</ref> The primary formation process for black holes is expected to be the [[gravitational collapse]] of heavy objects such as stars, but there are also more exotic processes that can lead to the production of black holes.
 
===Gravitational collapse===
{{Main|Gravitational collapse}}
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 [[degeneracy pressure]] of the star's constituents, condensing the matter in an exotic [[Degenerate matter|denser state]]. The result is one of the various types of [[compact star]]. The type of compact star formed depends on the mass of the remnant—the matter left over after the outer layers have been blown away, such from a [[supernova]] explosion or by pulsations leading to a [[planetary nebula]]. Note that this mass can be substantially less than the original star—remnants exceeding 5 solar masses are produced by stars that were over 20 solar masses before the collapse.<ref name="Carroll5.8"/>
 
If the mass of the remnant exceeds about 3–4 solar masses (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 [[neutrons]] is insufficient to stop the collapse. No known mechanism (except possibly quark degeneracy pressure, see [[quark star]]) 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 10<sup>3</sup> solar masses. These black holes could be the seeds of the supermassive black holes found in the centers of most galaxies.<ref name="ReesVolonteri">{{Cite book
|first1 = M. J. |last1=Rees
|first2 = M. |last2=Volonteri
|chapter= Massive black holes: formation and evolution
|title = Black Holes from Stars to Galaxies—Across the Range of Masses
|editor1-first=V. | editor1-last=Karas
|editor2-first=G. | editor2-last=Matt
|pages = 51–58
|publisher = Cambridge University Press
|year = 2007
|isbn =978-0-521-86347-6
|arxiv = astro-ph/0701512
}}</ref>
 
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 sees 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. |authorlink1=Roger Penrose
|title=Gravitational Collapse: The Role of General Relativity
|journal=General Relativity and Gravitation
|volume=34
|issue=7 |page=1141 |year=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
|ref=harv }}</ref>
 
====Primordial black holes in the Big Bang====
Gravitational collapse requires great density. In the current epoch of the universe these high densities are only found in stars, but in the early universe shortly after the [[big bang]] densities were much greater, possibly allowing for the creation of black holes. The high density alone is not enough to allow the formation of black holes since a uniform mass distribution will not allow the mass to bunch up. In order for [[primordial black holes]] to form in such a dense medium, there must be initial density perturbations that can then grow under their own gravity. Different models for the early universe vary widely in their predictions of the size of these perturbations. Various models predict the creation of black holes, ranging from a [[Planck mass]] to hundreds of thousands of solar masses.<ref>{{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
|publisher=Universal Academy Press
|year=2005
|isbn=4-946443-94-0
|arxiv=astro-ph/0511743
}}</ref> Primordial black holes could thus account for the creation of any type of black hole.
 
===High-energy collisions===
[[File:CMS Higgs-event.jpg|thumb|right|A simulated event in the CMS detector, a collision in which a micro black hole may be created.]]
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
|last=Giddings |first=S. B.
|last2=Thomas |first2=S.
|title=High energy colliders as black hole factories: The end of short distance physics
|year=2002
|journal=Physical Review D
|volume=65
|issue=5 |page=056010
|doi=10.1103/PhysRevD.65.056010
|arxiv=hep-ph/0106219
|ref=harv|bibcode = 2002PhRvD..65e6010G }}</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]] (''m''<sub>P</sub> = {{radic|''[[reduced Planck constant|ħ]][[speed of light|c]]''/''[[gravitational constant|G]]''}} ≈ {{val|1.2|e=19|ul=GeV/c2}} ≈ {{val|2.2|e=-8|u=kg}}), 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 |page=084004 |year=2006
|doi=10.1103/PhysRevD.74.084004
|arxiv=gr-qc/0609055
|bibcode = 2006PhRvD..74h4004H
|ref=harv }}</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 Planck mass could be much lower: some [[braneworld]] scenarios for example put the boundary as low as {{val|1|u=TeV/c2}}.<ref>{{Cite journal
|last=Arkani–Hamed |first=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 |page=263 |year=1998
|arxiv=hep-ph/9803315
|doi=10.1016/S0370-2693(98)00466-3
|ref=harv
|bibcode = 1998PhLB..429..263A }}</ref> This would make it conceivable for [[micro black hole]]s to be created in the high-energy collisions occurring when [[cosmic ray]]s hit the Earth's atmosphere, or possibly in the new [[Large Hadron Collider]] at [[CERN]]. Yet these theories are very speculative, and the creation of black holes in these processes is deemed unlikely by many specialists.<ref name="LHCsafety">{{cite web
|url=http://lsag.web.cern.ch/lsag/LSAG-Report.pdf
|title=Review of the Safety of LHC Collisions
|author=LHC Safety Assessment Group
|publisher=CERN
}}</ref> Even if micro black holes should be formed in these collisions, it is expected that they would [[black hole evaporation|evaporate]] in about 10<sup>−25</sup> 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 |year=2010
|url=http://www.einstein-online.info/spotlights/accelerators_bh/
|publisher=[[Max Planck Institute for Gravitational Physics|Max Planck Institute for Gravitational Physics (Albert Einstein Institute)]]
|ref=harv
}}</ref>
 
===Growth===
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 direct surroundings and omnipresent [[cosmic background radiation]]. This is the primary process through which supermassive black holes seem to have grown.<ref name="ReesVolonteri"/> A similar process has been suggested for the formation of [[intermediate-mass black hole]]s 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 |year=2010
|doi=10.1088/2041-8205/713/1/L41
|arxiv=1003.3470
|bibcode = 2010ApJ...713L..41V
|ref=harv }}</ref>
 
Another possibility is for a black hole to merge with other objects such as stars or even other black holes. Although not necessary for growth, this is thought to have been important, especially for the early development of supermassive black holes, which could have formed from the coagulation of many smaller objects.<ref name="ReesVolonteri"/> The process has also been proposed as the origin of some [[intermediate-mass black hole]]s.<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 |year=2004
|doi=10.1038/nature02448
|pmid=15085124
|arxiv = astro-ph/0402622 |bibcode = 2004Natur.428..724P
|pages=724–6
|ref=harv }}</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 |page=937 |year=2006
|doi=10.1086/498446
|arxiv=astro-ph/0508224 |bibcode=2006ApJ...637..937O
|ref=harv
}}</ref>
 
===Evaporation===
{{Main|Hawking radiation}}
In 1974, Hawking showed that black holes are not entirely black but emit small amounts of thermal radiation;<ref name=Hawking1974>{{Cite journal
|last=Hawking |first=S. W. | authorlink1= Stephen Hawking
|title=Black hole explosions?
|journal=Nature
|year=1974 |volume=248
|issue=5443 |pages=30–31
|doi=10.1038/248030a0
|ref=harv
|bibcode = 1974Natur.248...30H }}</ref> an effect that 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 in 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 |page=203 |year=2005
|arxiv=hep-th/0409024
|doi=10.1088/1367-2630/7/1/203
|ref=harv
|bibcode = 2005NJPh....7..203P }}</ref> If Hawking's theory of black hole radiation is correct, then black holes are expected to shrink and evaporate over time because 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 one solar mass has a Hawking temperature of about 100&nbsp;[[nanokelvin]]s. 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 shrink. To have a Hawking temperature larger than 2.7&nbsp;K (and be able to evaporate), a black hole needs to have less mass than the [[Moon]]. Such a black hole would have a diameter of less than a tenth of a millimeter.<ref>{{cite web
|url=http://www.einstein-online.info/elementary/quantum/evaporating_bh/?set_language=en
|title=Evaporating black holes?
|work=Einstein online
|publisher=Max Planck Institute for Gravitational Physics
|year=2010
|accessdate=2010-12-12
}}</ref>
 
If a black hole is very small the radiation effects are expected to become very strong. Even a black hole that is heavy compared to a human would evaporate in an instant. A black hole the weight of a car would have a diameter of about 10<sup>−24</sup>&nbsp;m and take a nanosecond to evaporate, during which time it would briefly have a luminosity 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</sup> would take less than 10<sup>−88</sup> seconds to evaporate completely. For such a small black hole, [[quantum gravity|quantum gravitation]] effects are expected to play an important role and could even—although current developments in quantum gravity do not indicate so<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|year=2008
|doi=10.1103/PhysRevD.78.035009
|arxiv=0806.3381
|bibcode = 2008PhRvD..78c5009G
|ref=harv }}</ref>—hypothetically make such a small black hole stable.<ref>{{cite journal
|last1=Peskin |first1=M. E.
|title=The end of the world at the Large Hadron Collider?
|journal=Physics
|volume=1|page=14|year=2008
|doi=10.1103/Physics.1.14
|bibcode = 2008PhyOJ...1...14P
|ref=harv }}
</ref>
 
==Observational evidence==
[[File:Images of gas cloud being ripped apart by the black hole at the centre of the Milky Way ESO.jpg|thumb|Images of gas cloud being ripped apart by the black hole at the centre of the [[Milky Way]].<ref>{{cite news|title=Ripped Apart by a Black Hole|url=http://www.eso.org/public/news/eso1332/|accessdate=19 July 2013|newspaper=ESO Press Release}}</ref> ]]
 
By their very nature, black holes do not directly emit any signals other than the hypothetical Hawking radiation; since the Hawking radiation for an astrophysical black hole is predicted to be very weak, this makes it impossible to directly detect astrophysical black holes from the Earth. A possible exception to the Hawking radiation being weak is the last stage of the evaporation of light (primordial) black holes; searches for such flashes in the past have proven unsuccessful and provide stringent limits on the possibility of existence of light primordial black holes.<ref>{{Cite journal
|last1=Fichtel |first1=C. E.
|last2=Bertsch |first2=D. L.
|last3=Dingus |first3=B. L.
|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 |year=1994
|doi=10.1086/174758
|ref=harv |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
|accessdate=2008-09-16
}}</ref>
 
Astrophysicists searching for black holes thus have to rely on indirect observations. A black hole's existence can sometimes be inferred by observing its gravitational interactions with its surroundings. [[Event Horizon Telescope|A project]] run by MIT's [[Haystack Observatory]] is attempting to observe the event horizon of a black hole directly. Initial results are encouraging.<ref>{{cite web |url= http://www.haystack.mit.edu/ast/uvlbi/mm/eht.html |title= Event Horizon Telescope |publisher= MIT Haystack Observatory |accessdate= 6 April 2012 }}</ref>
 
===Accretion of matter===
{{See also|Accretion disc}}
[[File:A star is consumed by a black hole.ogv|thumb|upright=1.2|A computer simulation of a star being consumed by a black hole. The blue dot indicates the location of the black hole.]]
 
Due to [[conservation of angular momentum]], gas falling into the [[gravitational well]] created by a massive object will typically form a disc-like structure around the object. Friction within the disc causes angular momentum to be transported outward, allowing matter to fall further inward, 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.
|contribution=Black Hole Binaries
|editor1-first=W. |editor1-last=Lewin
|editor2-first=M. |editor2-last=van der Klis
|title=Compact Stellar X-ray Sources
|year=2006
|publisher=Cambridge University Press
|isbn=0-521-82659-4
|arxiv=astro-ph/0306213
}} section 4.1.5.</ref> In the case of [[compact object]]s such as [[white dwarf]]s, [[neutron star]]s, and black holes, the gas in the inner regions becomes so hot that it will emit vast amounts of radiation (mainly X-rays), which 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 in radiation.<ref name=McClintockRemillard2006/> (In nuclear fusion only about 0.7% of the rest mass will be emitted as energy.) In many cases, accretion discs are accompanied by [[relativistic jets]] emitted along the poles, which carry away much of the energy. The mechanism for the creation of these jets is currently not well understood.
 
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 nucleus|active galactic nuclei]] and [[quasar]]s are believed to be the accretion discs 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 hole]]s.<ref>{{Cite journal
|last=Winter |first=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
|year=2006
|journal=The Astrophysical Journal
|volume=649 |issue=2 |page=730
|arxiv=astro-ph/0512480
|doi=10.1086/506579
|ref=harv |bibcode=2006ApJ...649..730W
}}</ref>
 
===X-ray binaries===
{{See also|X-ray binary}}
 
[[X-ray binaries]] are [[binary star]] systems that are luminous in the [[X-ray]] part of the spectrum. These X-ray emissions are generally thought to be caused by one of the component stars being a compact object accreting matter from the other (regular) star. The presence of an ordinary star in such a system provides a unique opportunity for studying the central object and determining if it might be a black hole.
 
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 obtain an estimate for the mass of the compact object. If this is much larger than the Tolman–Oppenheimer–Volkoff limit (that is, the maximum mass a neutron star can have before 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 |year=1999
|arxiv=astro-ph/9912186
|doi = 10.1088/0264-9381/16/12A/301
|ref=harv
}}</ref>
 
[[File:RXTE Detects Heartbeat Of Smallest Black Hole Candidate.ogv|thumb|This animation compares the X-ray 'heartbeats' of GRS 1915 and IGR J17091, two black holes that ingest gas from companion stars.]]
The first strong candidate for a black hole, [[Cygnus X-1]], was discovered in this way by [[Charles Thomas Bolton]],<ref>{{Cite journal
|last=Bolton |first=C. T.
|title=Identification of Cygnus X-1 with HDE 226868
|journal=Nature
|volume=235
|issue=5336 |pages=271–273 |year=1972
|doi=10.1038/235271b0
|ref=harv|bibcode = 1972Natur.235..271B }}</ref> Louise Webster and Paul Murdin<ref>{{Cite journal
|last1=Webster |first1=B. L.
|last2=Murdin |first2=P.
|title= Cygnus X-1—a Spectroscopic Binary with a Heavy Companion ?
|journal=Nature
|volume=235
|issue=5332 |pages=37–38 |year=1972
|doi=10.1038/235037a0
|ref=harv
|bibcode = 1972Natur.235...37W }}</ref> in 1972.<ref>{{cite web
|last=Rolston |first=B.
|date=10 November 1997
|url=http://news.utoronto.ca/bin/bulletin/nov10_97/art4.htm
|archiveurl=http://web.archive.org/web/20080502230214/http://news.utoronto.ca/bin/bulletin/nov10_97/art4.htm
|archivedate=2008-05-02
|title=The First Black Hole
|work=The bulletin
|publisher=University of Toronto
|accessdate=2008-03-11
}}</ref><ref>{{Cite journal
|last=Shipman |first=H. L.
|title=The implausible history of triple star models for Cygnus X-1 Evidence for a black hole
|journal=Astrophysical Letters
|date=1 January 1975
|volume=16|issue=1|pages=9–12
|bibcode=1975ApL....16....9S
|doi=10.1016/S0304-8853(99)00384-4
|ref=harv
|first2=Z
|first3=Y.W
}}</ref> Some doubt, however, remained due to the uncertainties resultant from the companion star being much heavier than the candidate black hole.<ref name="CMS1999"/> Currently, better candidates for black holes are found in a class of X-ray binaries called soft X-ray transients.<ref name="CMS1999"/> In this class of system the companion star is relatively low mass allowing for more accurate estimates in the black hole mass. Moreover, these systems are only active in X-ray for several months once every 10–50 years. During the period of low X-ray emission (called quiescence), the accretion disc is extremely faint allowing for detailed observation of the companion star during this period. One of the best such candidates is [[V404 Cyg]].
 
====Quiescence and advection-dominated accretion flow====
The faintness of the accretion disc during quiescence is suspected to be caused by the flow entering a mode called an [[advection-dominated accretion flow]] (ADAF). In this mode, almost all the energy generated by friction in the disc is swept along with the flow instead of radiated away. If this model is correct, then it forms strong qualitative evidence for the presence of an event horizon.<ref>{{cite journal
|last1=Narayan |first1=R.
|last2=McClintock|first2=J.
|title=Advection-dominated accretion and the black hole event horizon
|journal=New Astronomy Reviews
|volume=51
|issue=10–12|page=733|year=2008
|doi=10.1016/j.newar.2008.03.002
|bibcode = 2008NewAR..51..733N |arxiv = 0803.0322
|ref=harv }}</ref> Because, if the object at the center of the disc had a solid surface, it would emit large amounts of radiation as the highly energetic gas hits the surface, an effect that is observed for neutron stars in a similar state.<ref name=McClintockRemillard2006/>
 
====Quasi-periodic oscillations====
{{main|Quasi-periodic oscillations}}
 
The X-ray emission from accretion disks sometimes flickers at certain frequencies. These signals are called [[quasi-periodic oscillations]] 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 potential black holes.<ref>{{cite press release
|title=NASA scientists identify smallest known black hole
|publisher=[[Goddard Space Flight Center]]
|date=2008-04-01
|url=http://www.eurekalert.org/pub_releases/2008-04/nsfc-nsi040108.php
|accessdate=2009-03-14
}}</ref>
 
===Galactic nuclei===
{{See also| Active galactic nucleus}}
 
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. 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|gas]] and [[interstellar dust|dust]] called an accretion disk; and two [[relativistic jet|jets]] that are perpendicular to the accretion disk.<ref name="krolik1999">{{Cite book
|first=J. H. |last=Krolik
|year=1999
|title=Active Galactic Nuclei
|publisher=Princeton University Press
|isbn=0-691-01151-6
|at=Ch. 1.2
|url=http://books.google.com/?id=oRK8otMiWIgC&printsec=frontcover&dq=Active+Galactic+Nuclei#v=onepage&q&f=false
}}</ref><ref name="sparkegallagher2000">{{Cite book
|first=L. S. |last=Sparke
|first2=J. S. |last2=Gallagher
|year=2000
|title=Galaxies in the Universe: An Introduction
|publisher=Cambridge University Press
|at=Ch. 9.1
|url=http://books.google.com/?id=N8Hngab5liQC&printsec=frontcover&dq=Galaxies+in+the+Universe:+An+Introduction#v=onepage&q&f=false
|isbn=0-521-59740-4
}}</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
|first=J. |last=Kormendy
|first2=D. |last2=Richstone
|title=Inward Bound—The Search For Supermassive Black Holes In Galactic Nuclei
|journal=Annual Reviews of Astronomy and Astrophysics
|year=1995 |volume=33
|issue=1 |pages=581–624
|bibcode=1995ARA&A..33..581K
|doi=10.1146/annurev.aa.33.090195.003053
|ref=harv
}}</ref>
 
It is now widely accepted that the center 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 |year=2003
|doi=10.1086/379143
|arxiv=astro-ph/0308342
|ref=harv |bibcode=2003ApJ...596L..27K
}}</ref> The close observational correlation between the mass of this hole and the velocity dispersion of the host galaxy's [[bulge (astronomy)|bulge]], known as the [[M-sigma relation]], strongly suggests a connection between the formation of the black hole and the galaxy itself.<ref name="msigma2000">{{Cite journal
|title=A Fundamental Relation Between Supermassive Black Holes and their Host Galaxies
|last=Ferrarese |first=L.
|last2=Merritt |first2=D. |author2-link = David Merritt
|journal = The Astrophysical Journal Letters
|volume = 539| issue = 1| pages = 9–12 |year= 2000
|bibcode=2000ApJ...539L...9F
|doi=10.1086/312838
|arxiv=astro-ph/0006053
|ref=harv
}}</ref>
 
[[File:A simulation of how a gas cloud that has been observed approaching the supermassive black hole at the centre of the galaxy.jpg|thumb|Simulation of gas cloud after close approach to the black hole at the centre of the Milky Way.<ref>{{cite news|title=A Black Hole's Dinner is Fast Approaching|url=http://www.eso.org/public/news/eso1151/|accessdate=6 February 2012|newspaper=ESO Press Release}}</ref>]]
 
Currently, the best evidence for a supermassive black hole comes from studying the [[proper motion]] of stars near the center of our own [[Milky Way]].<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|page=1075|year=2009
|doi=10.1088/0004-637X/692/2/1075
|arxiv=0810.4674
|bibcode=2009ApJ...692.1075G
|ref=harv
}}</ref> Since 1995 astronomers have tracked the motion of 90 stars in a region called [[Sagittarius A*]]. By fitting their motion to [[Keplerian orbit]]s they were able to infer in 1998 that 2.6 million [[solar mass]]es must be contained in a volume with a radius of 0.02 [[lightyear]]s.<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|page=678|year=1998
|doi=10.1086/306528
|arxiv=astro-ph/9807210 |bibcode=1998ApJ...509..678G
|ref=harv
}}</ref> Since then one of the stars—called [[S2 (star)|S2]]—has completed a full orbit. From the orbital data they were able to place better constraints on the mass and size of the object causing the orbital motion of stars in the Sagittarius A* region, finding that there is a spherical mass of 4.3 million solar masses contained within a radius of less than 0.002 lightyears.<ref name="Gillessen"/> While this is more than 3000 times the Schwarzschild radius corresponding to that mass, it is at least consistent with the central object being a supermassive black hole, and no "realistic cluster [of stars] is physically tenable".<ref name="Ghez1998"/>
 
===Effects of strong gravity===
Another way that the black hole nature of an object may be tested in the future is through observation of effects caused by strong gravity in their vicinity. One such effect is [[gravitational lensing]]: The deformation of spacetime around a massive object causes light rays to be deflected much like light passing through an optic [[Lens (optics)|lens]].  Observations have been made of weak gravitational lensing, in which light rays are deflected by only a few [[arcseconds]]. However, it has never been directly observed for a black hole.<ref name="Bozza"/> One possibility for observing gravitational lensing by a black hole would be to observe stars in orbit around 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=42 |year=2010 |pages=2269–2300
|doi=10.1007/s10714-010-0988-2
|bibcode = 2010GReGr..42.2269B
|volume=42
|ref=harv }}</ref>
 
Another option would be the direct observation of gravitational waves produced by an object falling into a black hole, for example a compact object falling into a supermassive black hole through an [[extreme mass ratio inspiral]]. Matching the observed waveform to the predictions of general relativity would allow precision measurements of the mass and angular momentum of the central object, while at the same time testing general relativity.<ref>{{cite journal
|first1=L. |last1=Barack
|first2=C. |last2=Cutler
|title=LISA capture sources: Approximate waveforms, signal-to-noise ratios, and parameter estimation accuracy
|journal=Physical Review D |issue=69 |year=2004 |page=082005
|doi=10.1103/PhysRevD.69.082005
|arxiv=gr-qc/0310125
|bibcode = 2004PhRvD..69h2005B
|volume=69
|ref=harv }}</ref> These types of events are a primary target for the proposed [[Laser Interferometer Space Antenna]].
 
===Alternatives===
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 star]]s,<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
|year=2009 |volume=400 |issue=3 |pages=1632–1642
|doi=10.1111/j.1365-2966.2009.15571.x
|arxiv=0908.2672
|bibcode=2009MNRAS.400.1632K
|ref=harv}}</ref> and some [[supersymmetry|supersymmetric]] models predict the existence of [[Q star]]s.<ref>{{cite arXiv
|eprint=hep-ph/0612159
|first1=A. |last=Kusenko
|title=Properties and signatures of supersymmetric Q-balls
|class=hep-ph
|year=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|page= 1|year= 2005
|doi= 10.1016/j.physletb.2005.04.034
|arxiv=astro-ph/0410417
|bibcode = 2005PhLB..616....1H
|ref=harv }}</ref> These hypothetical models could potentially explain a number of observations of stellar black hole candidates. However, it can be shown from general 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 10<sup>8</sup> solar mass 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 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 no black holes).<ref>{{cite journal
|last1=Kiefer |first1=C.
|title=Quantum gravity: general introduction and recent developments
|journal=Annalen der Physik
|volume=15
|issue=1–2 |page=129 |year=2006
|doi=10.1002/andp.200510175
|arxiv=gr-qc/0508120
|bibcode = 2006AnP...518..129K
|ref=harv }}</ref> In 2002,<ref>http://forum.wolframscience.com/archive/topic/1688-1.html</ref> much attention has been drawn by the [[Fuzzball (string theory)|fuzzball]] model in [[string theory]]. Based on calculations in specific situations in string theory, the proposal suggests that generically the individual states of a black hole solution do not have an event horizon or singularity, but that for a classical/semi-classical observer the statistical average of such states does appear just like an ordinary black hole in 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 |year=2008
|doi=10.1016/j.physrep.2008.08.001
|arxiv=0804.0552
|bibcode = 2008PhR...467..117S
|ref=harv }}</ref>
 
==Open questions==
 
===Entropy and thermodynamics===
{{Further2|[[Black hole thermodynamics]]}}
[[File:BHentropy.svg|thumb|right|alt=S=1/4 k c<sup>3</sup>ħ<sup>−1</sup>G<sup>−1</sup> A.|The formula for the [[Bekenstein–Hawking entropy]] (S) of a black hole, which depends on the area of the black hole (A). The constants are the [[speed of light]] (c), the [[Boltzmann constant]] (k), [[Newton's constant]] (G), and the [[reduced Planck constant]] (ħ).]]
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 |year=1971
|doi=10.1103/PhysRevLett.26.1344
|bibcode=1971PhRvL..26.1344H
|ref=harv
}}</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 a 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 of 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=6 |year=2001
|arxiv=gr-qc/9912119
|url=http://relativity.livingreviews.org/Articles/lrr-2001-6/
|accessdate=2011-02-10
|bibcode = 1999gr.qc....12119W
|pages=12119
|doi=10.12942/lrr-2001-6
|ref=harv }}</ref>
 
The link with the laws of thermodynamics was further strengthened by Hawking's discovery 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, however 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
|first=G. |last='t Hooft
|chapter=The Holographic Principle
|title=Basics and highlights in fundamental physics
|series=Subnuclear series
|volume=37
|editor-last=Zichichi |editor-first=A.
|year=2001
|publisher=World Scientific
|isbn=978-981-02-4536-8
|arxiv=hep-th/0003004
}}</ref>
 
Although general relativity can be used to perform a semi-classical 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 (physics)|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 [[supersymmetry|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 |page=99 |year=1996
|doi=10.1016/0370-2693(96)00345-0
|arxiv=hep-th/9601029
|bibcode = 1996PhLB..379...99S
|ref=harv }}</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 journal
|last1=Carlip |first1=S.
|title=Black Hole Thermodynamics and Statistical Mechanics
|journal=Lecture Notes in Physics
|volume=769 |page=89 |year=2009
|doi=10.1007/978-3-540-88460-6_3
|arxiv=0807.4520
|series=Lecture Notes in Physics
|isbn=978-3-540-88459-0
|ref=harv
}}</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. 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
|work=www.hawking.org.uk
|accessdate=2009-03-14
}}</ref>
 
The question whether information is truly lost in black holes (the [[black hole information paradox]]) has divided the theoretical physics community (see [[Thorne–Hawking–Preskill bet]]). In quantum mechanics, loss of information corresponds to the violation of vital property called [[unitarity (physics)|unitarity]], which has to do with the conservation of probability. 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
|booktitle=Particles, Strings and Cosmology
|year=1995
|conference=Johns Hopkins Workshop on Current Problems in Particle Theory 19 and  the PASCOS Interdisciplinary Symposium 5
}}</ref> 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
|year=2011
|conference=XXV International Symposium on Lepton Photon Interactions at High Energies
|arxiv=1201.2079
}}</ref>
 
==See also==
{{Portal|Star}}
{{div col|colwidth=20em}}
* [[Black brane]]
* [[Black hole complementarity]]
* [[Black hole starship]]
* [[Black holes in fiction]]
* [[Black string]]
* [[BTZ black hole]]
* [[Dumb hole]]
* [[General relativity]]
* [[Kugelblitz (astrophysics)]]
* [[List of black holes]]
* [[Susskind-Hawking battle]]
* [[Timeline of black hole physics]]
* [[White hole]]
* [[Wormhole]]
 
{{div col end}}
 
==Notes==
<references group="Note"/>
 
==References==
{{Reflist|colwidth=30em}}
 
==Further reading==
;Popular reading
* {{Cite book| last1=Ferguson | first1=Kitty|title=Black Holes in Space-Time|publisher=Watts Franklin|year=1991|isbn=0-531-12524-6 |ref=harv}}
* {{Cite book|first1=Stephen |last1=Hawking |author1-link=Stephen Hawking|title=[[A Brief History of Time]]|publisher=Bantam Books, Inc|year=1988|isbn=0-553-38016-8|ref=harv}}
* {{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 |year=1996 |publisher=Princeton University Press |isbn=0-691-03791-4 |url=http://books.google.com/?id=LstaQTXP65cC |ref=harv}}
* {{Cite book| last1=Melia |first1=Fulvio | author1-link=Fulvio Melia |title=The Black Hole at the Center of Our Galaxy|publisher=Princeton U Press|year=2003|isbn=978-0-691-09505-9 |ref=harv}}
* {{Cite book| last1=Melia | first1=Fulvio |title=The Edge of Infinity. Supermassive Black Holes in the Universe|publisher=Cambridge U Press|year=2003|isbn=978-0-521-81405-8 |ref=harv}}
* {{Cite book| last1=Pickover | first1=Clifford|title=Black Holes: A Traveler's Guide|publisher=Wiley, John & Sons, Inc|year=1998|isbn=0-471-19704-1}}
* {{Cite book| last1=Thorne | first1=Kip S. |author-link=Kip Thorne|title=[[Black Holes and Time Warps]]|publisher=Norton, W. W. & Company, Inc|year=1994|isbn=0-393-31276-3|ref=harv}}
* {{Cite book| last=Wheeler |first=J. Craig|title = Cosmic Catastrophes|edition = 2nd|publisher = Cambridge University Press|year = 2007|isbn = 0-521-85714-7 |ref=harv}}
 
;University textbooks and monographs
* {{Cite book|last1=Carroll |first1=Sean M. |title=Spacetime and Geometry |year=2004 |publisher=Addison Wesley |isbn=0-8053-8732-3 |ref=harv}}, the lecture notes on which the book was based are available for free from Sean Carroll's [http://pancake.uchicago.edu/~carroll/notes/ website].
* {{Cite book|last1=Carter |first1=B. |authorlink1=Brandon Carter |year=1973 |chapter=Black hole equilibrium states |title=Black Holes |editor-last=DeWitt |editor-first=B. S. |editor1-link=Bryce De Witt |editor2-last=DeWitt |editor2-first=C. |ref=harv}}
* {{Cite book| last1=Chandrasekhar | first1=Subrahmanyan |authorlink1=Subrahmanyan Chandrasekhar |title=Mathematical Theory of Black Holes|publisher=Oxford University Press|year=1999|isbn=0-19-850370-9 |ref=harv}}
* {{Cite journal|last1=Frolov |first1=V. P. |last2=Novikov |first2=I. D. |year=1998 |title=Black hole physics |ref=harv}}
* {{Cite book |last1=Frolov |first1=Valeri P. |last2=Zelnikov |first2=Andrei |title=Introduction to Black Hole Physics |publisher=Oxford University Press |year=2011 |location=Oxford |url=http://books.google.com/books?id=r_l5AK9DdXsC&lpg=PA34 |isbn=978-0-19-969229-3 |zbl=1234.83001 |ref=harv}}
* {{Cite book| last1=Hawking |first1=S. W. |last2=Ellis |first2=G. F. R. |authorlink1=Stephen Hawking |title=Large Scale Structure of space time |publisher=Cambridge University Press |year=1973 |url=http://books.google.com/?id=QagG_KI7Ll8C |isbn=0-521-09906-4|ref=harv}}
* {{Cite book| last1=Melia |first1=Fulvio |author1-link=Fulvio Melia|title=The Galactic Supermassive Black Hole|publisher=Princeton U Press|year=2007|isbn=978-0-691-13129-0 |ref=harv}}
* {{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 | year=2000|isbn=0-201-38423-X |ref=harv}}
* {{Cite book|last1=Thorne | first1=Kip S. |last2=Misner | first2=Charles |last3=Wheeler | first3=John |author1-link=Kip Thorne |author2-link=Charles W. Misner| author3-link=John Archibald Wheeler |title=Gravitation|publisher=W. H. Freeman and Company|year=1973|isbn=0-7167-0344-0 |ref=harv}}
* {{cite book|last=Wald | first=Robert M. |author-link=Robert Wald |title=General Relativity |publisher=University of Chicago Press |year=1984 |isbn=978-0-226-87033-5 |url=http://books.google.com/books?id=9S-hzg6-moYC |ref=harv}}
* {{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| year=1992|isbn=0-226-87029-4 |ref=harv}}
 
;Review papers
* {{cite journal|last1=Gallo|first1=Elena|last2=Marolf|first2=Donald|doi=10.1119/1.3056569|title=Resource Letter BH-2: Black Holes|year=2009|page=294|issue=4|volume=77|journal=American Journal of Physics|arxiv=0806.2316|bibcode = 2009AmJPh..77..294G|ref=harv }}
* {{cite arXiv |eprint=hep-ph/0511217 |last1=Hughes|first1=Scott A. |title=Trust but verify: The case for astrophysical black holes |class=hep-ph |year=2005}} Lecture notes from 2005 [[SLAC]] Summer Institute.
 
==External links==
{{Sister project links|voy=no|wikt=no|commons=Category:Black holes|b=General Astronomy/Black holes/Introduction}}
* {{In Our Time|Black Holes|p00547f4|Black_Holes}}
* [[Stanford Encyclopedia of Philosophy]]: "[http://plato.stanford.edu/entries/spacetime-singularities/ Singularities and Black Holes]" by Erik Curiel and Peter Bokulich.
* "[http://www.scholarpedia.org/article/Black_hole Black hole]" on Scholarpedia.
* [http://hubblesite.org/explore_astronomy/black_holes/ Black Holes: Gravity's Relentless Pull]—Interactive multimedia Web site about the physics and astronomy of black holes from the Space Telescope Science Institute
* [http://apod.nasa.gov/htmltest/gifcity/bh_pub_faq.html Frequently Asked Questions (FAQs) on Black Holes]
* "[http://casa.colorado.edu/~ajsh/schwp.html Schwarzschild Geometry]"
* [http://library.thinkquest.org/C007571/english/advance/core8.htm Advanced Mathematics of Black Hole Evaporation]
* [http://hubblesite.org/explore_astronomy/black_holes/home.html Hubble site]
;Videos
* [http://www.eso.org/public/videos/eso0846b/ 16-year long study tracks stars orbiting Milky Way black hole]
* [http://web.archive.org/web/20040925044354/http://www.mpe.mpg.de/ir/GC/index.php Movie of Black Hole Candidate from Max Planck Institute]
{{Black holes|state=uncollapsed}}
{{Relativity}}
{{String theory topics}}
{{Good article}}
{{Use dmy dates|date=March 2011}}
 
{{DEFAULTSORT:Black Hole}}
[[Category:Black holes| ]]
[[Category:Galaxies]]
[[Category:Theory of relativity]]
 
{{Link FA|ml}}
{{Link GA|ar}}
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{{Link GA|ru}}
{{Link GA|tr}}
{{Link FA|vi}}

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