Extremal horizons in Einstein-Maxwell theory

The Einstein equations for a spacetime containing an extremal black hole impose restrictions on the horizon that can be studied independently of the exterior spacetime. The intrinsic structure of the horizon is described by the near-horizon geometry.

I will introduce near-horizon geometries and present intrinsic analogues of Hawking's topology and rigidity theorems. In particular, I will show that any non-trivial extremal horizon in four-dimensional Einstein-Maxwell theory is given by the extremal Kerr-Newman family. Part of this talk is based on joint work with David Katona and James Lucietti.