Editing Black hole (section)

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

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

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

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

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

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

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

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

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

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