Rigidity of stationary black holes with small angular momentum on the horizon

TL;DR

This paper proves that slowly rotating stationary vacuum black holes are isometric to Kerr solutions if the stationary Killing vector-field is small on the bifurcation sphere, establishing a rigidity result under small angular momentum conditions.

Contribution

It establishes a rigidity theorem for stationary vacuum black holes with small angular momentum, showing they are isometric to Kerr solutions.

Findings

Stationary vacuum black holes with small angular momentum are isometric to Kerr solutions.

The domain of outer communications of such black holes matches that of Kerr solutions.

Smallness of the stationary Killing vector-field on the bifurcation sphere is key to the rigidity.

Abstract

We prove a black hole rigidity result for slowly rotating stationary solutions of the Einstein vacuum equations. More precisely, we prove that the domain of outer communications of a regular stationary vacuum is isometric to the domain of outer communications of a Kerr solution, provided that the stationary Killing vector-field $\T$ is small on the bifurcation sphere.