Uniqueness of smooth stationary black holes in vacuum: small perturbations of the Kerr spaces

TL;DR

This paper proves that small perturbations of Kerr black holes in vacuum do not produce new solutions, confirming the uniqueness of Kerr black holes under such conditions.

Contribution

It establishes that any regular stationary vacuum black hole close to Kerr is actually identical to Kerr, confirming the stability and uniqueness of Kerr solutions.

Findings

Any small perturbation of Kerr isometric to Kerr itself

Supports the stability of Kerr black holes

Confirms the uniqueness of Kerr in vacuum solutions

Abstract

We prove that a regular stationary black-hole solution of the Einstein vacuum equations which is "close" to some Kerr solution is, in fact, isometric to that Kerr solution.