Geometric inequalities for axially symmetric black holes

Details Geometric inequalities for axially symmetric black holes Geometric inequalities for axially symmetric black holes

2011-11-15

arxiv.org/abs/1111.3615v2

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

65 pages, 5 figures. Review article, to appear in Class. Quantum Grav. as Topical Review. Improved presentation, minor correct

Scientific paper

A geometric inequality in General Relativity relates quantities that have both a physical interpretation and a geometrical definition. It is well known that the parameters that characterize the Kerr-Newman black hole satisfy several important geometric inequalities. Remarkably enough, some of these inequalities also hold for dynamical black holes. This kind of inequalities play an important role in the characterization of the gravitational collapse, they are closed related with the cosmic censorship conjecture. Axially symmetric black holes are the natural candidates to study these inequalities because the quasi-local angular momentum is well defined for them. We review recent results in this subject and we also describe the main ideas behind the proofs. Finally, a list of relevant open problem is presented.

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