0 Geometric characterisations of the Kerr isolated horizon

The quasi-local theory of black-holes uses isolated horizons, rather then entire space-times. Each isolated horizon is described by its geometry: the induced metric and parallel transport. The space of the geometries is infinite dimensional. On the other hand, the isolated horizons defined by the Kerr metric form a 2-dimensional subfamily. In this letter we derive geometric conditions on an isolated horizon that distinguish the geometries defined by the Kerr solution. 1 Isolated horizons. In the quasi-local description of black holes the role of an event horizon is played by so called isolated horizon[3, 1, 4], that is a null 3-surface