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\section*{Bekenstein-Hawking entropy}

\hypertarget{context}{}\subsubsection*{{Context}}\label{context}

\hypertarget{gravity}{}\paragraph*{{Gravity}}\label{gravity}

[[!include gravity contents]]

\hypertarget{physics}{}\paragraph*{{Physics}}\label{physics}

[[!include physicscontents]]

\hypertarget{contents}{}\section*{{Contents}}\label{contents}

\noindent\hyperlink{idea}{Idea}\dotfill \pageref*{idea} \linebreak
\noindent\hyperlink{properties}{Properties}\dotfill \pageref*{properties} \linebreak
\noindent\hyperlink{interpretation_in_adscft_correspondence}{Interpretation in AdS/CFT correspondence}\dotfill \pageref*{interpretation_in_adscft_correspondence} \linebreak
\noindent\hyperlink{interpretation_by_strong_coupling_limit_of_dbranes}{Interpretation by strong coupling limit of D-branes}\dotfill \pageref*{interpretation_by_strong_coupling_limit_of_dbranes} \linebreak
\noindent\hyperlink{related_concepts}{Related concepts}\dotfill \pageref*{related_concepts} \linebreak
\noindent\hyperlink{References}{References}\dotfill \pageref*{References} \linebreak
\noindent\hyperlink{ReferencesGeneral}{General}\dotfill \pageref*{ReferencesGeneral} \linebreak
\noindent\hyperlink{via_wickrotated_thermal_field_theory}{Via Wick-rotated thermal field theory}\dotfill \pageref*{via_wickrotated_thermal_field_theory} \linebreak
\noindent\hyperlink{interpretation_in_string_theory}{Interpretation in string theory}\dotfill \pageref*{interpretation_in_string_theory} \linebreak
\noindent\hyperlink{interpretation_as_entanglement_entropy}{Interpretation as entanglement entropy}\dotfill \pageref*{interpretation_as_entanglement_entropy} \linebreak


\hypertarget{idea}{}\subsection*{{Idea}}\label{idea}

In [[gravity]], \textbf{Bekenstein-Hawking entropy} is an [[entropy]] assigned to [[black hole]], on the basis of laws of thermodynamics and observers outside black hole. It striking property is that it is proportional to the surface area of the balck hole's [[horizon]].

\hypertarget{properties}{}\subsection*{{Properties}}\label{properties}

\hypertarget{interpretation_in_adscft_correspondence}{}\subsubsection*{{Interpretation in AdS/CFT correspondence}}\label{interpretation_in_adscft_correspondence}

In the context of [[string theory]] BH entropy is explained by a version of the [[AdS/CFT correspondence]]. Here every [[black brane]] solution in [[supergravity]] is the strong-coupling limit of a [[D-brane]] [[worldvolume]] [[QFT]]. After [[Kaluza-Klein mechanism|KK-reduction]] these black brane configurations become ordinary [[black hole]]s. The [[entropy]] of the [[D-brane]] worldvolume theories on the [[event horizon]] turns out to coincide with the BH entropy of the corresponding black hole.

Detailed computations exist in particular for [[D1-brane]]/[[D5-brane]] systems. This is parts of the [[AdS/CFT correspondence]]. See (\hyperlink{AGMOO}{AGMOO, chapter 5}).

See also

\begin{itemize}%
\item [[holographic entanglement entropy]]


\item \emph{[[string theory results applied elsewhere]]}.



\end{itemize}
\hypertarget{interpretation_by_strong_coupling_limit_of_dbranes}{}\subsubsection*{{Interpretation by strong coupling limit of D-branes}}\label{interpretation_by_strong_coupling_limit_of_dbranes}

Another way to derive Bekenstein-Hawking entropy in [[string theory]] is by computing the entropy of weakly coupled open strings on D-brane configurations in flat [[Minkowski space]] which transmute as the coupling constant is increased to given (supersymmetric) black hole configurations. More on this is at \emph{[[black holes in string theory]]}.

\hypertarget{related_concepts}{}\subsection*{{Related concepts}}\label{related_concepts}

\begin{itemize}%
\item gravitational entropy

\begin{itemize}%
\item [[black hole radiation]]


\item \textbf{Bekenstein-Hawking entropy}


\item [[generalized second law of thermodynamics]]


\item [[black holes in string theory]]


\item [[holographic entanglement entropy]]



\end{itemize}

\item [[thermal quantum field theory]]



\end{itemize}
\hypertarget{References}{}\subsection*{{References}}\label{References}

\hypertarget{ReferencesGeneral}{}\subsubsection*{{General}}\label{ReferencesGeneral}

A textbook account is

\begin{itemize}%
\item [[Valeri Frolov]], Andrei Zelnikov, \emph{Introduction to black hole physics}, Oxford 2011

\end{itemize}
Review form the point of view of [[thermal field theory]]:

\begin{itemize}%
\item S.A. Fulling, S.N.M. Ruijsenaars, \emph{Temperature, periodicity and horizons}, Physics Reports Volume 152, Issue 3, August 1987, Pages 135-176 (\href{https://www1.maths.leeds.ac.uk/~siru/papers/p26.pdf}{pdf}, )

\end{itemize}
Basic introductory accounts include

\begin{itemize}%
\item [[Robert Wald]], \emph{The Thermodynamics of Black Holes} (\href{http://arxiv.org/abs/gr-qc/9912119}{arXiv:gr-qc/9912119})


\item [[Jacob Bekenstein]], \emph{\href{http://www.scholarpedia.org/article/Bekenstein-Hawking_entropy}{Bekenstein-Hawking entropy}}, (2008), Scholarpedia, 3(10):7375



\end{itemize}
A more general discussion which identifies thermodynamic properties of all [[horizons]] appearing on gravity (not just [[black hole]] horizons) was given in

\begin{itemize}%
\item [[Ted Jacobson]], \emph{Thermodynamics of Spacetime: The Einstein Equation of State}, Phys.Rev.Lett.75:1260-1263, 1995 (\href{http://arxiv.org/abs/gr-qc/9504004}{arXiv:gr-qc/9504004})

\end{itemize}
This article showed that under some assumptions the [[Einstein equations]] can even be \emph{derived} from identifying gravitational horizon area with [[entropy]] and them imposing laws of [[thermodynamics]].

For more comments and more references on this observation see

\begin{itemize}%
\item [[Thanu Padmanabhan]], \emph{Thermodynamical Aspects of Gravity: New insights}, Rep. Prog. Phys. 73 (2010) 046901 (\href{http://arxiv.org/abs/0911.5004}{arXiv:0911.5004})

\end{itemize}
(Later authors tried to argue that derivations like this show that gravity is not a fundamental force of nature such as [[electromagnetism]] or the [[strong nuclear force]], but rather an [[entropic force]] that arises only from more fundamental forces in a [[thermodynamic limit]]. This however remains at best unclear.)

Discussion of black hole entropy from entropy of [[conformal field theory]] associated with the horizon has been given in

\begin{itemize}%
\item [[Steve Carlip]], \emph{Entropy from Conformal Field Theory at Killing Horizons}, Class.Quant.Grav.16:3327-3348,1999 (\href{http://xxx.lanl.gov/abs/gr-qc/9906126}{arXiv:gr-qc/9906126})


\item [[Steve Carlip]], \emph{Horizon Constraints and Black Hole Entropy}, Class.Quant.Grav.22:1303-1312, 2005 (\href{http://arxiv.org/abs/hep-th/0408123}{arXiv:hep-th/0408123})



\end{itemize}
and reviewed in

\begin{itemize}%
\item [[Steve Carlip]], \emph{Horizon constraints and black hole entropy} (\href{http://arxiv.org/abs/gr-qc/0508071}{arXiv:gr-qc/0508071})


\item [[Steve Carlip]], \emph{Symmetries, Horizons, and Black Hole Entropy}, Gen.Rel.Grav.39:1519-1523,2007; Int.J.Mod.Phys.D17:659-664,2008 (\href{http://arxiv.org/abs/0705.3024}{arXiv:0705.3024})



\end{itemize}
Further developments on black hole entropy are in

\begin{itemize}%
\item [[Ashoke Sen]], \emph{Logarithmic Corrections to Schwarzschild and Other Non-extremal Black Hole Entropy in Different Dimensions}, JHEP04(2013)156 (\href{http://arxiv.org/abs/arXiv:1205.0971}{arXiv:arXiv:1205.0971})


\item Aitor Lewkowycz, [[Juan Maldacena]], \emph{Generalized gravitational entropy} (\href{http://arxiv.org/abs/1304.4926}{arXiv:1304.4926})



\end{itemize}
A related controversial article that spawned a lot of discussion is

\begin{itemize}%
\item [[Ahmed Almheiri]], [[Donald Marolf]], [[Joseph Polchinski]], James Sully, \emph{Black holes: complementarity or firewalls?}, (\href{http://arxiv.org/abs/arXiv:1207.3123}{arXiv:1207.3123})

\end{itemize}
\hypertarget{via_wickrotated_thermal_field_theory}{}\subsubsection*{{Via Wick-rotated thermal field theory}}\label{via_wickrotated_thermal_field_theory}

Discussion via [[Wick rotation]] to [[Euclidean field theory]] on spacetimes with compact/periodic Euclidean time ([[thermal field theory]] on [[curved spacetimes]]) is in

\begin{itemize}%
\item S.A. Fulling, S.N.M. Ruijsenaars, \emph{Temperature, periodicity and horizons}, Physics Reports Volume 152, Issue 3, August 1987, Pages 135-176 (\href{https://www1.maths.leeds.ac.uk/~siru/papers/p26.pdf}{pdf}, )


\item [[Gary Gibbons]], Malcolm J. Perry, \emph{Black Holes and Thermal Green Functions}, Vol. 358, No. 1695 (1978) (\href{https://www.jstor.org/stable/79482}{jstor:79482})



\end{itemize}
\hypertarget{interpretation_in_string_theory}{}\subsubsection*{{Interpretation in string theory}}\label{interpretation_in_string_theory}

Rieview of interpretation of [[black holes in string theory]] includes

\begin{itemize}%
\item [[Ofer Aharony]], S. S. Gubser, [[Juan Maldacena]], [[Hirosi Ooguri]], Y. Oz, Chapter 5 of \emph{Large N field theories, string theory and gravity}, \href{http://arxiv.org/abs/hep-th/9905111}{arXiv:hep-th/9905111}


\item [[Dieter Lüst]], Ward Vleeshouwers, sections 21-22 of \emph{Black Hole Information and Thermodynamics} (\href{https://arxiv.org/abs/1809.01403}{arXiv:1809.01403})


\item Sebastian De Haro, Jeroen van Dongen, Manus Visser, [[Jeremy Butterfield]], \emph{Conceptual Analysis of Black Hole Entropy in String Theory} (\href{https://arxiv.org/abs/1904.03232}{arXiv:1904.03232})


\item Jeroen van Dongen, Sebastian De Haro, Manus Visser, [[Jeremy Butterfield]], \emph{Emergence and Correspondence for String Theory Black Holes} (\href{https://arxiv.org/abs/1904.03234}{arXiv:1904.03234})



\end{itemize}
Discussion in view of [[higher curvature corrections]] includes

\begin{itemize}%
\item [[Thomas Mohaupt]], \emph{Strings, higher curvature corrections, and black holes} (\href{http://arxiv.org/abs/hep-th/0512048}{arXiv:hep-th/0512048})

\end{itemize}
See also

\begin{itemize}%
\item MO question, \href{http://mathoverflow.net/questions/31789/statistical-physics-of-string-theory}{statistical-physics-of-string-theory}

\end{itemize}
\hypertarget{interpretation_as_entanglement_entropy}{}\subsubsection*{{Interpretation as entanglement entropy}}\label{interpretation_as_entanglement_entropy}

Discussions of the interpreation of BH entropy as [[holographic entanglement entropy]] include

\begin{itemize}%
\item Alejandro Satz, [[Ted Jacobson]], \emph{Black hole entropy and the renormalization group} (\href{http://arxiv.org/abs/1301.3171}{arXiv:1301.3171})

\end{itemize}
Computation of [[black hole entropy]] in 4d via [[AdS4-CFT3 duality]] from [[holographic entanglement entropy]] in the [[ABJM theory]] for the [[M2-brane]] is discussed in

\begin{itemize}%
\item Jun Nian, Xinyu Zhang, \emph{Entanglement Entropy of ABJM Theory and Entropy of Topological Black Hole} (\href{https://arxiv.org/abs/1705.01896}{arXiv:1705.01896})

\end{itemize}
[[!redirects black hole entropy]] [[!redirects BH entropy]]

[[!redirects black hole thermodynamics]]



\end{document}