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\begin{document}

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\section*{black brane}

\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{weak_coupling_correspondence}{Weak coupling correspondence}\dotfill \pageref*{weak_coupling_correspondence} \linebreak
\noindent\hyperlink{examples}{Examples}\dotfill \pageref*{examples} \linebreak
\noindent\hyperlink{related_concepts}{Related concepts}\dotfill \pageref*{related_concepts} \linebreak
\noindent\hyperlink{references}{References}\dotfill \pageref*{references} \linebreak
\noindent\hyperlink{prehistory}{Prehistory}\dotfill \pageref*{prehistory} \linebreak
\noindent\hyperlink{general}{General}\dotfill \pageref*{general} \linebreak


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

The theory of [[gravity]] in $3+1$ dimensions famously has [[black hole]] solutions, being the limiting configuration of a \emph{point} mass gravitational source. In higher dimensional gravity, and in particular in higher dimensional [[supergravity]], there are analogous solutions, which however are limiting configurations of a gravitational source that is supported on a line, or a surface, or a higher dimensional space. For a surface one might speak of \emph{black [[membrane]]} solutions hence generally of \emph{black brane} solutions.

Particularly the [[BPS states]] among the black branes in [[supergravity]], i.e. those solutions that carry [[Killing spinors]], include configurations that look like the strong-coupling version of the [[Green-Schwarz super p-branes]].

[[!include black branes in supergravity -- table]]

The [[near-horizon geometry]] of these black branes is generically that of [[anti de Sitter spacetime]] times a [[sphere]]. To the extent that the [[worldvolume]] theory of the branes is a [[superconformal QFT]], this is the origin of the [[AdS-CFT correspondence]].

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

\hypertarget{weak_coupling_correspondence}{}\subsubsection*{{Weak coupling correspondence}}\label{weak_coupling_correspondence}

The types of black branes that can occur in theories of [[supergravity]] that are obtained from the maximal [[11-dimensional supergravity]] match precisely the types of [[D-brane]]s and [[NS-brane]]s that appear in the corresponding perturbative [[superstring theories]].

The idea is that both these brane-phenomena are aspects of one single entity:

\begin{itemize}%
\item At low [[string coupling]] the [[D-brane]]/[[NS-brane]] description is accurate. Low [[string coupling]] implies that the coupling of [[gravity]] is weak, hence that the back-reaction of the branes on the background geometry is negligible.


\item At large [[string coupling]] but low [[energy]], the [[effective field theory|effective]] [[supergravity]] description becomes accurate. Here the branes do back-react on the gravitational background and hence create the \emph{black brane} spacetime geometry.



\end{itemize}
This duality of the brane picture is at the heart of the [[AdS/CFT correspondence]]. See there for more details.

\hypertarget{examples}{}\subsection*{{Examples}}\label{examples}

\begin{itemize}%
\item [[black hole]], [[black hole in string theory]]


\item [[black string]]


\item [[black membrane]]


\item [[black fivebrane]]


\item [[string triple junction]]


\item [[membrane triple junction]]



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

[[!include table of branes]]

\hypertarget{references}{}\subsection*{{References}}\label{references}

\hypertarget{prehistory}{}\subsubsection*{{Prehistory}}\label{prehistory}

\begin{itemize}%
\item [[Albert Einstein]], [[Leopold Infeld]], B. Hoffmann, \emph{The gravitational equations and the problem of motion}, Annals of Mathematics, Vol 39, No. 1, 1938

\end{itemize}
See also

\begin{itemize}%
\item Wikipedia, \emph{\href{https://en.wikipedia.org/wiki/Black_hole_electron}{Black hole electron}}

\end{itemize}
\hypertarget{general}{}\subsubsection*{{General}}\label{general}

Original articles include

\begin{itemize}%
\item [[Michael Duff]], J. X. Lu, \emph{Black and super $p$-branes in diverse dimensions}, Nucl.Phys. B416 (1994) 301-334 (\href{http://arxiv.org/abs/hep-th/9306052}{arXiv:hep-th/9306052})


\item [[Mike Duff]], Ramzi R. Khuri, J. X. Lu, \emph{String Solitons}, Phys.Rept. 259:213-326, 1995 (\href{https://arxiv.org/abs/hep-th/9412184}{arXiv:hep-th/9412184})


\item [[Michael Duff]], H. Lu, [[Christopher Pope]], \emph{The Black Branes of M-theory}, Phys.Lett.B382:73-80,1996 (\href{http://arxiv.org/abs/hep-th/9604052}{arXiv:hep-th/9604052})



\end{itemize}
The [[M5-brane]] was maybe first found as a black brane of [[11-dimensional supergravity]] (the [[black fivebrane]]) in

\begin{itemize}%
\item [[Rahmi Gueven]], \emph{Black $p$-brane solutions of $D = 11$ supergravity theory, Phys. Lett. B276 (1992) 49 and in [[Mike Duff]] (ed.)}[[The World in Eleven Dimensions]]\_ 135-141 (\href{http://inspirehep.net/record/338203}{spire:338203})

\end{itemize}
The observation that black $p$-branes metric for \emph{odd} $p$ are completely non-singular is due to

\begin{itemize}%
\item [[Gary Gibbons]], [[Gary Horowitz]], [[Paul Townsend]], p. 15 of \emph{Higher-dimensional resolution of dilatonic black hole singularities}, Class. Quant. Grav.12:297-318,1995 (\href{https://arxiv.org/abs/hep-th/9410073}{arXiv:hep-th/9410073})

\end{itemize}
The suggestion that extremal/[[BPS state]] black branes are the strong coupling incarnation of fundamental branes originates in

\begin{itemize}%
\item [[Chris Hull]], [[Paul Townsend]], \emph{Unity of Superstring Dualities}, Nucl.Phys.B438:109-137,1995 (\href{http://arxiv.org/abs/hep-th/9410167}{arXiv:hep-th/9410167})


\item [[Edward Witten]], bottom of p. 6 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}
Review includes,

\begin{itemize}%
\item [[Mike Duff]], chapter 5 of \emph{[[The World in Eleven Dimensions]]: Supergravity, 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 [[Kellogg Stelle]], around section 3.3. of \emph{BPS Branes in Supergravity} (\href{http://arxiv.org/abs/hep-th/9803116}{arXiv:hep-th/9803116})


\item [[Ofer Aharony]], S.S. Gubser, [[Juan Maldacena]], H. Ooguri, Y. Oz, section 1.3 of \emph{Large N Field Theories, String Theory and Gravity} (\href{http://arxiv.org/abs/hep-th/9905111}{arXiv:hep-th/9905111})


\item [[Thomas Mohaupt]], \emph{Black holes in supergravity and string theory}, Class. Quantum Grav. 17 (2000) 3429--3482 (\href{http://www.itp.uni-hannover.de/~giulini/papers/BlackHoleSeminar/Mohaupt_CQG_2000.pdf}{pdf})


\item [[Ralph Blumenhagen]], [[Dieter Lüst]], [[Stefan Theisen]], \emph{Brane solutions in supergravity}, chapter 18.5 in \emph{Basic Concepts of String Theory} Part of the series Theoretical and Mathematical Physics pp 585-639 Springer 2013



\end{itemize}
and in the context of multiple [[M2-branes]] in the [[BLG model]]:

\begin{itemize}%
\item [[Jonathan Bagger]], [[Neil Lambert]], [[Sunil Mukhi]], Constantinos Papageorgakis, section 1.6 of \emph{Multiple Membranes in M-theory} (\href{http://arxiv.org/abs/1203.3546}{arXiv:1203.3546})

\end{itemize}
Further developments include

\begin{itemize}%
\item Gerard Clement, Dmitri Gal'tsov, Cedric Leygnac, \emph{Black branes on the linear dilaton background}, Phys. Rev. D71 (2005) 084014 (\href{http://arxiv.org/abs/hep-th/0412321}{arXiv:hep-th/0412321})


\item D. Gal'tsov, S. Klevtsov, D. Orlov, G. Clement, \emph{More on general $p$-brane solutions}, Int.J.Mod.Phys.A21:3575-3604, 2006 (\href{http://arxiv.org/abs/hep-th/0508070}{arXiv:hep-th/0508070})


\item [[Michael Duff]], \emph{Near-horizon brane scan revived}, Nucl. Phys. B810:193-209, 2009 (\href{http://arxiv.org/abs/0804.3675}{arXiv:0804.3675})


\item Jay Armas, Joan Camps, Troels Harmark, Niels A. Obers, \emph{The Young Modulus of Black Strings and the Fine Structure of Blackfolds} (\href{http://arxiv.org/abs/1110.4835}{arXiv:1110.4835})



\end{itemize}
[[!redirects black branes]] [[!redirects black p-brane]] [[!redirects black p-branes]]



\end{document}