Non-existence of stationary two-black-hole configurations

TL;DR

This paper proves that two aligned sub-extremal black holes cannot be in a stationary equilibrium due to the incompatibility of their physical constraints, resolving a longstanding question in black hole physics.

Contribution

The authors formulate a boundary value problem and use inverse scattering methods to demonstrate the non-existence of stationary two-black-hole configurations.

Findings

No stationary equilibrium configurations exist for two aligned sub-extremal black holes.

Universal inequality between angular momentum and horizon area is key to the proof.

The result rules out the possibility of balanced two-black-hole systems in this setting.

Abstract

We resume former discussions of the question, whether the spin-spin repulsion and the gravitational attraction of two aligned sub-extremal black holes can balance each other. To answer the question we formulate a boundary value problem for two separate (Killing-) horizons and apply the inverse (scattering) method to solve it. Making use of a universal inequality between angular momentum and horizon area that has to be satisfied by every sub-extremal black hole, we prove the non-existence of the equilibrium situation in question.