  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.

General Relativity and Quantum Cosmology;Analysis of PDEs