General Relativity pp 429-526 | Cite as

# Black Holes

## Abstract

This extended chapter of almost hundred pages on black hole physics is a central part of the book. We begin with Israel’s original demonstration of the statement that a static black hole solution of Einstein’s vacuum equation has to be spherically symmetric, and is thus a Schwarzschild black hole. Then a detailed derivation of the Kerr solution is given, that makes efficient use of Cartan’s calculus of differential forms. The properties of this rotating black hole solution, that ranks among the most important solutions of Einstein’s (vacuum) equations, are carefully analysed, and it is shown in a more general setting what is behind the results. Later, this is also used in derivations of the four laws of black hole dynamics, which are formally closely related to the main laws of thermodynamics. A section is devoted on accretion tori around Kerr black holes. Furthermore, we present the evidence for black holes in some X-ray binary systems and for supermassive black holes in galactic centres.

## Keywords

Black Hole Event Horizon Active Galactic Nucleus Kerr Black Hole Null Hypersurface## References

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