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

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.

Minor corrections, submitted version

References in corpus (4)

• On the uniqueness of smooth, stationary black holes in vacuum
• Uniqueness of smooth stationary black holes in vacuum: small perturbations of the Kerr spaces
• Uniqueness results for ill posed characteristic problems in curved space-times
• Has the black hole equilibrium problem been solved?

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• Uniqueness of Kerr-Newman-de Sitter black holes with small angular momenta
• Algorithmic characterization results for the Kerr-NUT-(A)dS space-time. I. A space-time approach