Non-existence of stationary two-black-hole configurations: The degenerate case

TL;DR

This paper proves that stationary configurations of two extremal black holes cannot exist, extending previous results that showed non-existence for sub-extremal black holes, thus confirming the impossibility of such equilibrium states.

Contribution

It extends the non-existence proof of stationary two-black-hole configurations to include extremal black holes, using boundary value problem solutions and a new black hole criterion.

Findings

No stationary equilibrium of two extremal black holes exists.

The non-existence result applies to both sub-extremal and extremal cases.

The proof relies on boundary value problem analysis and a novel black hole criterion.

Abstract

In a preceding paper we examined the question whether the spin-spin repulsion and the gravitational attraction of two aligned sub-extremal black holes can balance each other. Based on the solution of a boundary value problem for two separate (Killing-) horizons and a novel black hole criterion we were able to prove the non-existence of the equilibrium configuration in question. In this paper we extend the non-existence proof to extremal black holes.