Stationary two-black-hole configurations: A non-existence proof

TL;DR

This paper proves that stationary, equilibrium configurations of two aligned rotating black holes cannot exist by analyzing boundary problems and black hole properties, extending inverse scattering methods to non-linear equations.

Contribution

It provides a rigorous non-existence proof for two-black-hole equilibrium configurations using advanced mathematical techniques.

Findings

No stationary two-black-hole equilibrium configurations exist.

The proof utilizes boundary problem solutions and violation of black hole properties.

Extends inverse scattering methods to non-linear elliptic equations in this context.

Abstract

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 equilibrium configurations consisting of two aligned rotating black holes. Our discussion is principally aimed at developing the ideas of the proof and summarizing the results of two preceding papers (Neugebauer and Hennig, 2009 [29], Hennig and Neugebauer, 2011 [12]). From a mathematical point of view, this paper is a further example (Meinel et al., 2008 [22]) for the application of the inverse ("scattering") method to a non-linear elliptic differential equation.