On the uniqueness of smooth, stationary black holes in vacuum
arXiv:0711.0040 · doi:10.1007/s00222-008-0146-6
Abstract
We prove a conditional "no hair" theorem for smooth manifolds: if $E$ is the domain of outer communication of a smooth, regular, stationary Einstein vacuum, and if a technical condition relating the Ernst potential and Killing scalar is satisfied on the bifurcate sphere, then $E$ is locally isometric to the domain of outer communication of a Kerr space-time.
Various corrections