Rotating and swirling binary black hole system balanced by its gravitational spin-spin interaction

TL;DR

This paper presents the first exact analytical solution in General Relativity for a balanced binary black hole system, where gravitational attraction is countered by spin-spin repulsion, modeled through a novel embedding into a swirling universe.

Contribution

It introduces a new exact solution describing two stationary extremal Kerr black holes in equilibrium, balanced by gravitational spin-spin interaction, using Ehlers transformation techniques.

Findings

The solution is completely regular outside the horizons.

Thermodynamic laws are verified for the system.

Microscopic entropy degrees of freedom are computed from dual CFT.

Abstract

We present the first exact and analytical solution in General Relativity describing an equilibrium configuration for two stationary black holes. The metric models two collinear extremal Kerr black holes immersed in an external and back-reacting rotating tidal drag. The gravitational attraction is balanced by the repulsive gravitational spin-spin interaction generated by the interplay between black holes angular momenta and the rotational background. The new solution is built by embedding the double Kerr metric into a swirling universe by means of the Ehlers transformation. The geometry is completely regular outside the event horizons. Thermodynamic properties of the binary black hole system are studied, the Smarr law, the first law and the Christodoulou-Ruffini formulas are verified. Microscopic degrees of freedom of the entropy are computed from the dual CFT living on the boundary of the near horizon geometries.