On the rigidity of stationary charged black holes: small perturbations of the non-extremal Kerr-Newman family

TL;DR

This paper proves that small perturbations of non-extremal Kerr-Newman black holes that are asymptotically flat and have bifurcate horizons must also be Kerr-Newman solutions, establishing a local uniqueness result.

Contribution

It provides a perturbative proof of the uniqueness of Kerr-Newman black holes using Mars-Simon type tensors to measure closeness.

Findings

Small perturbations close to Kerr-Newman are also Kerr-Newman.

The Mars-Simon tensors effectively detect deviations from Kerr-Newman.

The result applies to asymptotically flat space-times with bifurcate horizons.

Abstract

We prove a perturbative result concerning the uniqueness of Kerr-Newman family of black holes: given an asymptotically flat space-time with bifurcate horizons, if it agrees with a non-extremal Kerr-Newman space-time asymptotically flat at infinity and it is sufficiently close to the Kerr-Newman family, then the space-time must be one of the Kerr-Newman solutions. The closeness to the Kerr-Newman family is measured by the smallness of a pair of Mars-Simon type tensors, which were introduced by Wong in \cite{Wong_09} to detect the Kerr-Newmann family.