Stationary black-hole binaries: A non-existence proof

TL;DR

This paper proves that two aligned black holes cannot be in a stationary equilibrium due to the incompatibility of their gravitational and spin-spin interactions, using advanced mathematical methods.

Contribution

It provides a rigorous non-existence proof for stationary black-hole binaries with aligned spins, extending the application of inverse scattering techniques in non-linear gravity theories.

Findings

No stationary equilibrium configurations exist for aligned black-hole binaries.

The solution of a boundary problem reveals violations of black hole properties.

Demonstrates the effectiveness of inverse scattering methods in gravitational theory.

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. Based on the solution of a boundary problem for disconnected (Killing) horizons and the resulting violation of characteristic black hole properties, we present a non-existence proof for the equilibrium configuration in question. From a mathematical point of view, this result is a further example for the efficiency of the inverse ("scattering") method in non-linear theories.