Seminarium Teorii Względności i Grawitacji

The uniqueness theorems for asymptotically flat, static, black hole solutions to Einstein-Maxwell theory in four and higher dimensions are only valid for non-extreme black holes. In the extreme case the solution must belong to a generalised class of Majumdar-Papapetrou solutions. I will discuss recent work which establishes that the only spacetimes in this class, with a suitably regular event horizon, are the standard multi-black hole solutions. The proof involves a careful analysis of the near-horizon geometry and an extension of the positive mass theorem to Riemannian manifolds with conical singularities.