Equilibrium configuration of black holes and the inverse scattering method

Abstract

The inverse scattering method is applied to the investigation of the equilibrium configuration of black holes. A study of the boundary problem corresponding to this configuration shows that any axially symmetric, stationary solution of the Einstein equations with disconnected event horizon must belong to the class of Belinskii-Zakharov solutions. Relationships between the angular momenta and angular velocities of black holes are derived.

Stationary Black-Hole Binaries: A Non-existence Proof

“…Thus we could make use of results derived for the double-Kerr-NUT solution. The result is in line with a theorem of Varzugin [38,39], which says that the 2N-soliton solution by Belinskiȋ and Zakharov [4,5] contains all possible solutions (if any existed) corresponding to an equilibrium configuration of black holes. The subclass is characterized by a set of restrictions for the parameters of the general double-Kerr-NUT solution.…”

Stationary Black Holes: Uniqueness and Beyond

“…In any case, according to Varzugin [306,307] and, independently, to Neugebauer and Meinel [251] (a more detailed exposition can be found in [249,147]), the multi-soliton solutions provide the only candidates for stationary axisymmetric electrovacuum solutions. A breakthrough in the understanding of vacuum two-component configurations has been made by Hennig and Neugebauer [147,249], based on the area-angular momentum inequalities of Ansorg, Cederbaum and Hennig [145] as follows: Hennig and Neugebauer exclude many of the solutions by verifying that they have negative total ADM mass.…”

“…The third strategy to conclude the uniqueness proof has been advocated by Varzugin [306,307] and, independently, by Neugebauer and Meinel [251]. The idea is to exploit the properties of the linear problem associated with the harmonic map equations, discovered by Belinski and Zakharov [23,22] (see also [268]).…”

The interaction force between rotating black holes at equilibrium

“…The Einstein equations are then divided into two system of nonlinear equations, the first of which can be brought to the form 1) and the second one to the form…”