Non-existence of stationary two-black-hole configurations

TL;DR

This paper proves that two aligned black holes cannot be in a stationary equilibrium due to the imbalance of gravitational attraction and spin-spin repulsion, using inverse scattering methods and a novel criterion.

Contribution

The authors demonstrate the non-existence of stationary two-black-hole configurations with aligned spins through a boundary value problem and inverse scattering techniques.

Findings

No stationary equilibrium configurations exist for two aligned black holes.

The proof employs inverse scattering methods and a new black hole criterion.

The result clarifies limitations on black hole interactions in equilibrium.

Abstract

We resume former discussions of the question, whether the spin-spin repulsion and the gravitational attraction of two aligned 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 results of Manko, Ruiz and Sanabria-G\'omez and a novel black hole criterion, we prove the non-existence of the equilibrium situation in question.