Stationary Black-Hole Binaries: A Non-existence Proof

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.

Geometrical inequalities bounding angular momentum and charges in General Relativity

“…A very interesting application of the area-angular momentum inequality (174), with Q = 0, is the result by Neugebauer and Hennig (2009); Hennig and Neugebauer (2011); Neugebauer and Hennig (2012), and Neugebauer and Hennig (2014) where they prove that there does not exist a two black hole configuration in equilibrium. This problem has been open since the early days of General Relativity (see Neugebauer and Hennig 2014 for further references and Beig and Chruściel 1996;Beig and Schoen 2009;Manko et al 2011 for different approaches and results on the subject). The Neugebauer and Hennig argument is the following: Start out with the spacetime metric for an axially symmetric, stationary system containing two disconnected Killing horizons on the symmetry axis.…”

Geometric Inequalities for Black Holes

“…The results in theorem 3.2 has been used in a recent non-existence proof of stationary black holes binaries [67] [66] [22].…”