On the uniqueness of smooth, stationary black holes in vacuum

TL;DR

This paper proves a conditional uniqueness theorem for smooth, stationary vacuum black holes, showing they are locally isometric to Kerr solutions under certain technical conditions.

Contribution

It establishes a new conditional 'no hair' theorem for smooth, stationary Einstein vacuum spacetimes with specific technical conditions on the bifurcate sphere.

Findings

Under the specified conditions, the domain of outer communication is locally Kerr.

The theorem extends the class of known uniqueness results for black holes.

It provides a rigorous mathematical foundation for the uniqueness of Kerr black holes in vacuum.

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.