Geometric inequalities for black holes

SERGIO DAIN

Conferencia; Relativity and Gravitation, 100 years after Einstein in Prague,; 2012

It is well known that the parameters that characterize the Kerr 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. We briefly review recent results in this subject.