Uniqueness Theorems for Black Hole Space-Times

Abstract.

This lecture gives a brief outline of the proof of the black hole uniqueness theorem. Since the latter applies to stationary space-times, we first recall the reduction of the Einstein-Maxwell action in the presence of a Killing field. The resulting coset structure of the field equations gives rise to the Mazur identity, being the key to the uniqueness proof for the Kerr-Newman metric.