nLab no-hair theorem

Idea

In the context of gravity (general relativity and its variants, such as supergravity) what are called no-hair theorems are statements saying that or to which extent black hole spacetimes and more generally black brane spacetimes are characterized by their mass, angular momentum and charge, hence that they look much like macroscopic fundamental particles or fundamental branes (“black branes”).

Examples

In 4d Einstein-Maxwell theory

The archetypical example is 4-dimensional Einstein-Maxwell theory, where the no-hair theorem asserts that all black hole solutions are entirely characterized by their mass, angular momentum and electric charge.

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

In 4d Einstein-Yang-Mills theory

Generalizing to 4-dimensional Einstein-Yang-Mills theory with nonabelian gauge group, the situation becomes much more subtle. (…)

In higher supergravity

…

References

• Charles Misner, Kip Thorne, John Archibald Wheeler, pp. 875–876 of Gravitation, San Francisco: W. H. Freeman. (1973)

• Pawel O. Mazur, Black Uniqueness Theorems, Proceedings of the 11th International Conference on General Relativity and Gravitation, ed. M. A. H. MacCallum, Cambridge University Press, Cambridge 1987, pp. 130-157 (arXiv:hep-th/0101012)

• J. Lopes Costa, On black hole uniqueness theorems, 2010 (pdf)

• Stefan Hollands, Akihiro Ishibashi, Black hole uniqueness theorems in higher dimensional spacetimes, Classical and Quantum Gravity, Volume 29, Number 16 (arXiv:1206.1164)

See also

• Wikipedia, No-hair theorem