Seminarium Teorii Względności i Grawitacji

Killing horizon extremality condition, combined with Einstein's vacuum equations, induces equations that must be satisfied by the 2-dimensional geometry of the horizon section and the rotation vector field defined on it. The study of these equations leads to the theory of the intrinsic uniqueness of extreme black holes: the spherical topology of the global section (in the rotating case), rigidity, no-hair - all those properties are proved in turn. Extreme horizons in higher dimensional spacetimes also satisfy a similar equation and many results are still valid. In addition to a review of that intrinsic theory of extremal horizon new results will be presented: local rigidity of non-rotating extremal horizon and extremal horizons of the topology of three dimensional sphere.