Non-existence of multiple-black-hole solutions close to Kerr-Newman

TL;DR

This paper proves that near Kerr-Newman solutions cannot have multiple black holes without assuming axial symmetry, simplifying the conditions needed for black hole uniqueness.

Contribution

It demonstrates the non-existence of multi-black-hole solutions close to Kerr-Newman without axial symmetry assumptions.

Findings

Multiple-black-hole solutions near Kerr-Newman do not exist.

Axial symmetry is not required for the uniqueness proof.

Supports the perturbative uniqueness of Kerr black holes.

Abstract

We show that a stationary asymptotically flat electro-vacuum solution of Einstein's equations that is everywhere locally "almost isometric" to a Kerr-Newman solution cannot admit more than one event horizon. Axial symmetry is not assumed. In particular this implies that the assumption of a single event horizon in Alexakis-Ionescu-Klainerman's proof of perturbative uniqueness of Kerr black holes is in fact unnecessary.