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\section*{black holes in string theory}

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

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

[[!include gravity contents]]

\hypertarget{string_theory}{}\paragraph*{{String theory}}\label{string_theory}

[[!include string theory - contents]]

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

\noindent\hyperlink{black_hole_entropy}{Black hole entropy}\dotfill \pageref*{black_hole_entropy} \linebreak
\noindent\hyperlink{related_concepts}{Related concepts}\dotfill \pageref*{related_concepts} \linebreak
\noindent\hyperlink{References}{References}\dotfill \pageref*{References} \linebreak
\noindent\hyperlink{introductions_and_review}{Introductions and Review}\dotfill \pageref*{introductions_and_review} \linebreak
\noindent\hyperlink{original_articles}{Original articles}\dotfill \pageref*{original_articles} \linebreak
\noindent\hyperlink{black_holes_in_supergravity}{Black holes in supergravity}\dotfill \pageref*{black_holes_in_supergravity} \linebreak
\noindent\hyperlink{discussion_in_bfss_matrix_theory}{Discussion in BFSS matrix theory}\dotfill \pageref*{discussion_in_bfss_matrix_theory} \linebreak
\noindent\hyperlink{relation_to_topological_string_amplitudes}{Relation to topological string amplitudes}\dotfill \pageref*{relation_to_topological_string_amplitudes} \linebreak


\hypertarget{black_hole_entropy}{}\subsection*{{Black hole entropy}}\label{black_hole_entropy}

In ([[perturbative string theory|perturbative]]) [[string theory]] the [[Bekenstein-Hawking entropy]] associated to a macroscopic [[black hole]] finds an explanation as follows:

The [[black hole]] [[spacetime]] is regarded as a [[non-perturbative QFT|strongly coupled]] [[condensate]] of string states ([[closed strings]], carrying [[gravity]]). One looks for a corresponding weakly-coupled background for closed strings in flat [[Minkowski space]] that is known to turn into the black hole spacetime as the [[string coupling]] is turned on. Such turn out to be certain [[D-brane]] configurations in Minkowski space: at weak coupling the D-brane does not back-react on the spacetime (since that back-reaction is mediated by closed string quanta) and so it just sits there, whereas at strong coupling it curves spacetime and may collapse to a configuration that looks like the prescribed black hole spacetime.



\begin{quote}%
graphics grabbed from \hyperlink{IbanezUranga12}{Ibanez-Uranga 12}


\end{quote}
Now, if the configuration has a sufficient amount of [[supersymmetry]] preserved ([[BPS state]]), then one argues (\hyperlink{Witten95}{Witten 95, section 2.3}) that certain observables are actually independent of the coupling constant (``[[protection from quantum corrections]]''), and accordingly these observables are the same for black holes as for the corresponding D-brane configurations in flat space, where they may be computed in string perturbation theory.

The best studied such configuration is that of [[D1-D5 brane bound states]]. For these configurations one may compute the number of [[BPS states]] (which are ``protected''), hence the [[entropy]], via the [[Witten genus]] (\hyperlink{StromingerVafa96}{Strominger-Vafa 96}), see at \emph{\href{Witten+genus#RelationToBPSStateCounting}{Witten genus -- Relation to BPS state counting}}. By the above reasoning this may then be compared to the [[Bekenstein-Hawking entropy]] of the corresponding (supersymmetric) black hole. And indeed the results match the semiclassical BH-entropy to leading order and in addition provide their higher order quantum corrections. See the \emph{\hyperlink{References}{References}} below.

The [[T-duality|T-dual]] version of the D1/D5-bound states are D0/D6-bound states, coming from the [[Kaluza-Klein monopole]] in [[11-dimensional supergravity]] (e.g. \hyperlink{Nelson93}{Nelson 93}).

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

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


\item [[black ring]]


\item [[black brane]]

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


\item [[black string]]


\item [[black membrane]]


\item [[black fivebrane]]



\end{itemize}

\item [[AdS/CFT correspondence]]

\begin{itemize}%
\item [[Sachdev-Ye-Kitaev model]]

\end{itemize}

\item gravitational entropy

\begin{itemize}%
\item [[Bekenstein-Hawking entropy]]


\item [[generalized second law of thermodynamics]]


\item [[black holes in string theory]]


\item [[holographic entanglement entropy]]



\end{itemize}


\end{itemize}
[[!include table of branes]]

\begin{itemize}%
\item [[5d supergravity]]

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

A careful non-technical exposition is in

\begin{itemize}%
\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}
\hypertarget{introductions_and_review}{}\subsubsection*{{Introductions and Review}}\label{introductions_and_review}

\begin{itemize}%
\item [[Juan Maldacena]], \emph{Black Holes in String Theory}, PhD thesis 1996 (\href{http://arxiv.org/abs/hep-th/9607235}{arXiv:hep-th/9607235})


\item [[Juan Maldacena]], \emph{Black Holes and D-branes}, Nucl.Phys.Proc.Suppl. 61A (1998) 111-123; Nucl.Phys.Proc.Suppl. 62 (1998) 428-442 (\href{http://arxiv.org/abs/hep-th/9705078}{arXiv:hep-th/9705078})


\item [[Mike Duff]], chapter 5 of \emph{[[The World in Eleven Dimensions]]: Supgergravity, Supermembranes and M-theory}, IoP 1999 (\href{https://www.crcpress.com/The-World-in-Eleven-Dimensions-Supergravity-supermembranes-and-M-theory/Duff/9780750306720}{publisher})


\item [[Kostas Skenderis]], \emph{Black holes and branes in string theory}, Lect.Notes Phys. 541 (2000) 325-364 (\href{https://arxiv.org/abs/hep-th/9901050}{arXiv:hep-th/9901050})


\item [[Thomas Mohaupt]], \emph{Black Hole Entropy, Special Geometry and Strings}, Fortsch.Phys. 49 (2001) 3-161 (\href{http://arxiv.org/abs/hep-th/0007195}{arXiv:hep-th/0007195})


\item Sumit R. Das, [[Samir Mathur]], \emph{The Quantum Physics of Black Holes: Results from String Theory} (\href{http://arxiv.org/abs/gr-qc/0105063}{arXiv:gr-qc/0105063})


\item Justin R. David, Gautam Mandal, Spenta R. Wadia, \emph{Microscopic Formulation of Black Holes in String Theory} (\href{http://arxiv.org/abs/hep-th/0203048}{arXiv:hep-th/0203048})


\item [[Thibault Damour]], \emph{The entropy of black holes: a primer} (\href{http://arxiv.org/abs/hep-th/0401160}{arXiv:hep-th/0401160})


\item [[Barton Zwiebach]], chapter 22 of \emph{A first course in string theory}


\item [[Per Kraus]], \emph{Lectures on black holes and the AdS}3 / CFT\_2 correspondence\_ (\href{http://arxiv.org/abs/hep-th/0609074}{arXiv:hep-th/0609074})

\emph{Stringy black holes in five dimensions}, 2007 (\href{http://hep.ps.uci.edu/~arajaram/Irvine.07.pdf}{pdf slides})


\item [[Xi Yin]], \emph{Black Holes, Anti de Sitter space, and Topological Strings}, 2006 (\href{http://www.people.fas.harvard.edu/~xiyin/Site/Research_files/allthesis.pdf}{pdf})


\item [[Ashoke Sen]], \emph{Black Hole Entropy Function, Attractors and Precision Counting of Microstates}, extensive lecture notes (\href{http://arxiv.org/abs/0708.1270}{arXiv:0708.1270})


\item Joao Gomes, \emph{Quantum entropy of supersymmetric black holes} (\href{http://arxiv.org/abs/1111.2025}{arXiv:1111.2025})


\item [[Luis Ibáñez]], [[Angel Uranga]], section 6.2 of \emph{[[String Theory and Particle Physics -- An Introduction to String Phenomenology]]}, Cambridge University Press 2012


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


\item [[Alberto Zaffaroni]], \emph{Lectures on AdS Black Holes, Holography and Localization} (\href{https://arxiv.org/abs/1902.07176}{arXiv:1902.07176})



\end{itemize}
Lectures on AdS Black Holes, Holography and Localization Alberto Zaffaroniee also

\begin{itemize}%
\item \href{http://www.stringwiki.org}{String Theory Wiki}, \emph{\href{http://www.stringwiki.org/w/index.php?title=Black_Hole_Entropy}{Black hole entropy}}

\end{itemize}
\hypertarget{original_articles}{}\subsubsection*{{Original articles}}\label{original_articles}

The argument that properties of [[BPS states]] are preserved as the coupling increases beyond [[perturbation theory]] and are not destroyed by [[non-perturbative effects]] originates in

\begin{itemize}%
\item [[Edward Witten]], section 2.3 of \emph{String Theory Dynamics In Various Dimensions}, Nucl.Phys.B443:85-126,1995 (\href{http://arxiv.org/abs/hep-th/9503124}{arXiv:hep-th/9503124})

\end{itemize}
The original computations of stringy black hole entropy using this argument are due to

\begin{itemize}%
\item [[Ashoke Sen]], \emph{Extremal black holes and elementary string states} (\href{http://arxiv.org/abs/hep-th/9504147}{arXiv:hep-th/9504147})


\item [[Andrew Strominger]], [[Cumrun Vafa]], \emph{Microscopic Origin of the Bekenstein-Hawking Entropy} (\href{http://arxiv.org/abs/hep-th/9601029}{arXiv:hep-th/9601029})


\item Curtis Callan, [[Juan Maldacena]], \emph{D-brane Approach to Black Hole Quantum Mechanics} (\href{http://arxiv.org/abs/hep-th/9602043}{arXiv:hep-th/9602043})


\item [[Juan Maldacena]], [[Gregory Moore]], [[Andrew Strominger]], \emph{Counting BPS Blackholes in Toroidal Type II String Theory} (\href{http://arxiv.org/abs/hep-th/9903163}{arXiv:hep-th/9903163})


\item [[Davide Gaiotto]], [[Andrew Strominger]], X. Yin, \emph{New Connections Between 4D and 5D Black Holes}, JHEP 0602:024,2006 (\href{http://arxiv.org/abs/hep-th/0503217}{arXiv:hep-th/0503217})



\end{itemize}
See also

\begin{itemize}%
\item [[Emil Martinec]], V. Sahakian, \emph{Black Holes and Five-brane Thermodynamics}, Phys.Rev. D60 (1999) 064002 (\href{http://arxiv.org/abs/hep-th/9901135}{arXiv:hep-th/9901135})

\end{itemize}
Discussion for [[M-theory]]/[[11-dimensional supergravity]] includes

\begin{itemize}%
\item [[Juan Maldacena]], [[Andrew Strominger]], [[Edward Witten]], \emph{Black Hole Entropy in M-Theory}, JHEP 9712:002,1997 (\href{http://arxiv.org/abs/hep-th/9711053}{arXiv:hep-th/9711053})


\item [[Gary Horowitz]] , M. Roberts, \emph{Counting the microstates of a Kerr black hole in M theory}, Phys Rev Lett. 2007 Nov 30;99(22):221601. Epub 2007 Nov 30. (\href{https://www.ncbi.nlm.nih.gov/pubmed/18233277}{web}), (\href{https://arxiv.org/abs/0708.1346}{arXiv:0708.1346})


\item [[Davide Gaiotto]], [[Andrew Strominger]], Xi Yin, \emph{The M5-Brane Elliptic Genus: Modularity and BPS States}, JHEP 0708:070,2007 (\href{http://arxiv.org/abs/hep-th/0607010}{arXiv:hep-th/0607010})



\end{itemize}
Discussion relating to the [[Kaluza-Klein monopole]] includes

\begin{itemize}%
\item William Nelson, \emph{Kaluza-Klein Black Holes in String Theory}, Phys.Rev.D49:5302-5306,1994 (\href{http://arxiv.org/abs/hep-th/9312058}{arXiv:hep-th/9312058})

\end{itemize}
More recent developments include

\begin{itemize}%
\item Alejandra Castro, Joshua L. Davis, [[Per Kraus]], Finn Larsen, \emph{String Theory Effects on Five-Dimensional Black Hole Physics} (\href{http://arxiv.org/abs/0801.1863}{arXiv:0801.1863})


\item Oleg Lunin, [[Samir Mathur]], \emph{A toy black hole S-matrix in the D1-D5 CFT} (\href{http://arxiv.org/abs/1211.5830}{arXiv:1211.5830})


\item Alejandra Castro, Joshua M. Lapan, Alexander Maloney, Maria J. Rodriguez, \emph{Black Hole Monodromy and Conformal Field Theory} (\href{http://arxiv.org/abs/1303.0759}{arXiv:1303.0759})


\item Francesco Benini, Paolo Milan, \emph{Black holes in 4d $\mathcal{N} = 4$ Super-Yang-Mills} (\href{https://arxiv.org/abs/1812.09613}{arXiv:1812.09613})


\item H. L. Dao, Parinya Karndumri, \emph{Supersymmetric $AdS_5$ black holes and strings from 5D $N=4$ gauged supergravity} (\href{https://arxiv.org/abs/1812.10122}{arXiv:1812.10122})


\item Sunjin Choi, Joonho Kim, Seok Kim, June Nahmgoong, \emph{Large AdS black holes from QFT} (\href{https://arxiv.org/abs/1810.12067}{arxiv:1810.12067})



\end{itemize}
\hypertarget{black_holes_in_supergravity}{}\subsubsection*{{Black holes in supergravity}}\label{black_holes_in_supergravity}

Black holes in [[supergravity]]:

\begin{itemize}%
\item [[Riccardo D'Auria]], [[Pietro Fre]], \emph{BPS black holes in supergravity}, (\href{http://arxiv.org/abs/hep-th/9812160}{hep-th/9812160})


\item Antonio Gallerati, \emph{Constructing black hole solutions in supergravity theories} (\href{https://arxiv.org/abs/1905.04104}{arXiv:1905.04104})



\end{itemize}
\hypertarget{discussion_in_bfss_matrix_theory}{}\subsubsection*{{Discussion in BFSS matrix theory}}\label{discussion_in_bfss_matrix_theory}

Discussion of black holes via the [[BFSS matrix model]] includes the following:

\begin{itemize}%
\item [[Tom Banks]], [[Willy Fischler]], [[Igor Klebanov]], [[Leonard Susskind]], \emph{Schwarzschild Black Holes from Matrix Theory}, Phys.Rev.Lett.80:226-229,1998 (\href{https://arxiv.org/abs/hep-th/9709091}{arXiv:hep-th/9709091})


\item [[Tom Banks]], [[Willy Fischler]], [[Igor Klebanov]], [[Leonard Susskind]], \emph{Schwarzchild Black Holes in Matrix Theory II}, JHEP 9801:008,1998 (\href{https://arxiv.org/abs/hep-th/9711005}{arXiv:hep-th/9711005})


\item [[Igor Klebanov]], [[Leonard Susskind]], \emph{Schwarzschild Black Holes in Various Dimensions from Matrix Theory}, Phys.Lett.B416:62-66,1998 (\href{https://arxiv.org/abs/hep-th/9709108}{arXiv:hep-th/9709108})


\item Edi Halyo, \emph{Six Dimensional Schwarzschild Black Holes in M(atrix) Theory} (\href{https://arxiv.org/abs/hep-th/9709225}{arXiv:hep-th/9709225})


\item [[Gary Horowitz]], [[Emil Martinec]], \emph{Comments on Black Holes in Matrix Theory}, Phys. Rev. D 57, 4935 (1998) (\href{https://arxiv.org/abs/hep-th/9710217}{arXiv:hep-th/9710217})


\item Daniel Kabat, [[Washington Taylor]], \emph{Spherical membranes in Matrix theory}, Adv.Theor.Math.Phys.2:181-206,1998 (\href{https://arxiv.org/abs/hep-th/9711078}{arXiv:hep-th/9711078})


\item Yoshifumi Hyakutake, \emph{Black Hole and Fuzzy Objects in BFSS Matrix Model} (\href{https://arxiv.org/abs/1801.07869}{arXiv:1801.07869})



\end{itemize}
\hypertarget{relation_to_topological_string_amplitudes}{}\subsubsection*{{Relation to topological string amplitudes}}\label{relation_to_topological_string_amplitudes}

Discussion of black hole microstates via the [[topological string]]`s [[Gopakumar-Vafa invariants]]:

\begin{itemize}%
\item [[Rajesh Gopakumar]], [[Cumrun Vafa]], \emph{M-Theory and Topological Strings--I} (\href{https://arxiv.org/abs/hep-th/9809187}{arXiv:hep-th/9809187})


\item [[Rajesh Gopakumar]], [[Cumrun Vafa]], \emph{M-Theory and Topological Strings--II} (\href{https://arxiv.org/abs/hep-th/9812127}{arXiv:hep-th/9812127})



\end{itemize}
[[!redirects black hole in string theory]]



\end{document}