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\begin{document}

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\section*{black hole}

\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{examples}{Examples}\dotfill \pageref*{examples} \linebreak
\noindent\hyperlink{properties}{Properties}\dotfill \pageref*{properties} \linebreak
\noindent\hyperlink{topology}{Topology}\dotfill \pageref*{topology} \linebreak
\noindent\hyperlink{entropy}{Entropy}\dotfill \pageref*{entropy} \linebreak
\noindent\hyperlink{empirical_observation}{Empirical observation}\dotfill \pageref*{empirical_observation} \linebreak
\noindent\hyperlink{examples_2}{Examples}\dotfill \pageref*{examples_2} \linebreak
\noindent\hyperlink{related_concepts}{Related concepts}\dotfill \pageref*{related_concepts} \linebreak
\noindent\hyperlink{references}{References}\dotfill \pageref*{references} \linebreak
\noindent\hyperlink{observation}{Observation}\dotfill \pageref*{observation} \linebreak
\noindent\hyperlink{review}{Review}\dotfill \pageref*{review} \linebreak
\noindent\hyperlink{in_supergravity}{In supergravity}\dotfill \pageref*{in_supergravity} \linebreak
\noindent\hyperlink{holographic_description}{Holographic description}\dotfill \pageref*{holographic_description} \linebreak
\noindent\hyperlink{cosmology_inside_black_holes}{Cosmology inside black holes}\dotfill \pageref*{cosmology_inside_black_holes} \linebreak


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

A \emph{black hole} is a [[spacetime]] that solves [[Einstein equations]] of [[general relativity]] characterized by the fact that it posseses an \textbf{[[event horizon]]} hypersurface (or several of them) which has a number of special characteristics; for example the light can not escape from the space confined by the horizon hypersurface due to [[gravity|gravitational]] effects. Much of the theoretical considerations are about the entropy of black holes (cf. [[Bekenstein-Hawking entropy]]) and the information paradox.

Black holes are considered theoretically for [[gravity|gravitational theories]] in various number $d$ of dimension. For $d \geq 5$ a black hole [[spacetime]] may have nontrivial [[topology]], e.g. \emph{[[black rings]]} are possible.

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

\begin{itemize}%
\item In usual asymptotically 3+1-dimensional [[Minkowski spacetime]], the first black hole solution that was found is the [[Schwarzschild black hole]] solution; such a black hole posses a single horizon hypersurface and seems to be stable under various perturbations.


\item Another solution with finite angular momentum is called the [[Kerr spacetime]], and there is a simple generalization having also the electric charge, the Newman solution or the Kerr-Newman black hole. This solution differs pretty much from the Schwarzschild solution and its structure is unstable under various physical mechanisms and perturbations; it possesses two horizons, inner and outer.



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

\hypertarget{topology}{}\subsubsection*{{Topology}}\label{topology}

Hawking's \emph{Theorem of Black Hole topology} asserts that the in case of $d = 4$ asymptotically flat stationary black holes satisfying the suitable [[dominant energy condition]], the cross sections of the [[event horizon]] are spherical.

\hyperlink{GallowaySchoen}{Galloway and Schoen} extended this theorem to higher dimensions; they showed that the cross sections of event horizon (stationary case) and the outer (apparent) horizon (general case) are of Yamabe type.

\hypertarget{entropy}{}\subsubsection*{{Entropy}}\label{entropy}

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


\item [[generalized second law of thermodynamics]]



\end{itemize}
\hypertarget{empirical_observation}{}\subsection*{{Empirical observation}}\label{empirical_observation}

See

\begin{itemize}%
\item [[observing black holes]].

\end{itemize}
Some candidate [[astrophysics|astrophysical]] objects which seem to point to black hole have been observed.

\hypertarget{examples_2}{}\subsection*{{Examples}}\label{examples_2}

[[!include charged and rotating black holes -- table]]

$\,$

\begin{itemize}%
\item [[black hole in anti-de Sitter spacetime]]

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

\begin{itemize}%
\item [[Schwarzschild radius]]


\item [[Kruskal–Szekeres coordinates]]


\item [[Bekenstein-Hawking entropy]], [[black hole radiation]]


\item [[Penrose-Hawking singularity theorem]], [[cosmic censorship hypothesis]]


\item [[extremal black hole]]


\item [[generalized second law of thermodynamics]]


\item [[black hole information paradox]]


\item [[black ring]]


\item [[black brane]], [[black holes in string theory]]


\item [[firewall problem]]



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

\hypertarget{observation}{}\subsubsection*{{Observation}}\label{observation}

Resolved image of the direct vicinity of the [[event horizon]] of the [[black hole]] in the center of the [[galaxy]] [[Messier 87]]:

\begin{itemize}%
\item [[Event Horizon Telescope Collaboration]], \emph{First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole}, The Astrophysical Journal Letters, Volume 875, Number 1, 2019 (\href{https://iopscience.iop.org/article/10.3847/2041-8213/ab0ec7}{doi:10.3847/2041-8213/ab0ec7})

\end{itemize}
\hypertarget{review}{}\subsubsection*{{Review}}\label{review}

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


\item wikipedia: \href{http://en.wikipedia.org/wiki/Black_hole}{black hole}


\item [[Croatian black hole school]], 2010


\item Barrett O'Neill, \emph{The geometry of Kerr black holes}


\item S. Chandrasekhar, \emph{The mathematical theory of black holes}


\item G. T. Horowitz, A. Strominger, \emph{Counting states of near-extremal black holes}, Phys. Rev. Lett. 77 (1996) 2368--2371, \href{http://arxiv.org/abs/hep-th/9602051}{hep-th/9602051}.


\item Gregory Galloway, Richard Schoen, \emph{A Generalization of Hawking's Black Hole Topology Theorem to Higher Dimensions} Commun. Math. Phys. (2006) (\href{http://www.math.miami.edu/~galloway/papers/220_2006_19_OnlinePDF.pdf}{pdf})



\end{itemize}
\begin{itemize}%
\item [[Robert Wald]], \emph{Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics}, University of Chicago Press 1994; \emph{The back reaction effect in particle creation in curved spacetime}, Commun. Math. Phys. \textbf{54}, 1 (1977)


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



\end{itemize}
\hypertarget{in_supergravity}{}\subsubsection*{{In supergravity}}\label{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{holographic_description}{}\subsubsection*{{Holographic description}}\label{holographic_description}

Discussion of black holes in the context of the [[holographic principle]] and the [[AdS-CFT correspondence]] is in

\begin{itemize}%
\item Monica Guica, Thomas Hartman, Wei Song, [[Andrew Strominger]], \emph{The Kerr/CFT Correspondence} (\href{http://arxiv.org/abs/0809.4266}{arXiv:0809.4266})


\item Alejandra Castro, Alexander Maloney, [[Andrew Strominger]], \emph{Hidden Conformal Symmetry of the Kerr Black Hole} (\href{http://arxiv.org/abs/1004.0996}{arXiv:1004.0996})



\end{itemize}
The nature of the [[event horizon]], specifically, is discussed in

\begin{itemize}%
\item Kyriakos Papadodimas, Suvrat Raju, \emph{An Infalling Observer in AdS/CFT} (\href{http://arxiv.org/abs/1211.6767}{arXiv:1211.6767})

\end{itemize}
\hypertarget{cosmology_inside_black_holes}{}\subsubsection*{{Cosmology inside black holes}}\label{cosmology_inside_black_holes}

\begin{itemize}%
\item Razieh Pourhasan, Niayesh Afshordi, Robert B. Mann, \emph{Out of the White Hole: A Holographic Origin for the Big Bang} (\href{https://arxiv.org/abs/1309.1487}{arxiv:1309.1487})

\end{itemize}
[[!redirects black holes]]

[[!redirects black hole spacetime]] [[!redirects black hole spacetimes]]



\end{document}