nLab black hole

Idea

A black hole is a spacetime that solves Einstein equations of general relativity characterized by the fact that it possesses an event horizon hypersurface (or several of them) which has a number of special characteristics, for example that light cannot escape from the space confined by the horizon hypersurface due to 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 gravitational theories in various number $d$ of dimension. For $d \geq 5$ a black hole spacetime may have nontrivial topology, e.g. black rings are possible.

Examples

• 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.

• 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.

Properties

Topology

Hawking’s 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.

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.

Entropy

• Bekenstein-Hawking entropy

• generalized second law of thermodynamics

Empirical observation

See

• observing black holes.

Some candidate astrophysical? objects which seem to point to black hole have been observed.

Examples

black hole spacetimes	vanishing angular momentum	positive angular momentum
vanishing charge	Schwarzschild spacetime	Kerr spacetime
positive charge	Reissner-Nordstrom spacetime	Kerr-Newman spacetime

$\,$

• black hole in anti-de Sitter spacetime

Related concepts

• supernova

• Schwarzschild radius

• Kruskal–Szekeres coordinates

• Bekenstein-Hawking entropy, black hole radiation

• Penrose-Hawking singularity theorem, cosmic censorship hypothesis

• extremal black hole

• generalized second law of thermodynamics

• black hole information paradox

• black ring

• black brane, black holes in string theory

• firewall problem

References

Observation

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

• Event Horizon Telescope Collaboration, First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole, The Astrophysical Journal Letters, Volume 875, Number 1, 2019 (doi:10.3847/2041-8213/ab0ec7)

Review

• Valeri Frolov, Andrei Zelnikov, Introduction to black hole physics, Oxford 2011

• Wikipedia, Black hole

• Croatian black hole school, 2010

• S. Chandrasekhar, The mathematical theory of black holes

• G. T. Horowitz, A. Strominger, Counting states of near-extremal black holes, Phys. Rev. Lett. 77 (1996) 2368–2371, hep-th/9602051.

• Gregory Galloway, Richard Schoen, A Generalization of Hawking’s Black Hole Topology Theorem to Higher Dimensions Commun. Math. Phys. (2006) (pdf)

• Robert Wald, Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics, University of Chicago Press 1994; The back reaction effect in particle creation in curved spacetime, Commun. Math. Phys. 54, 1 (1977)

• Pietro Fré, Gravity, a Geometrical Course, Volume 2: Black Holes, Cosmology and Introduction to Supergravity, Springer (2013) [doi:10.1007/978-94-007-5443-0]

With focus on regular black holes:

• Chen Lan, Hao Yang, Yang Guo, Yan-Gang Miao, Regular black holes: A short topic review [arXiv:2303.11696]

In supergravity

Black holes in supergravity:

• Riccardo D'Auria, Pietro Fre, BPS black holes in supergravity, (hep-th/9812160)

• Antonio Gallerati, Constructing black hole solutions in supergravity theories (arXiv:1905.04104)

Holographic description

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

• Monica Guica, Thomas Hartman, Wei Song, Andrew Strominger, The Kerr/CFT Correspondence, Phys. Rev. D 80 (2009) 124008 [arXiv:0809.4266, doi:10.1103/PhysRevD.80.124008]

• Alejandra Castro, Alexander Maloney, Andrew Strominger, Hidden Conformal Symmetry of the Kerr Black Hole (arXiv:1004.0996)

The nature of the event horizon, specifically, is discussed in

• Kyriakos Papadodimas, Suvrat Raju, An Infalling Observer in AdS/CFT (arXiv:1211.6767)

Cosmology inside black holes

• Razieh Pourhasan, Niayesh Afshordi, Robert B. Mann, Out of the White Hole: A Holographic Origin for the Big Bang (arxiv:1309.1487)