Exact solution for the simplest binary system of Kerr black holes

TL;DR

This paper derives an explicit analytical solution for a system of two counter-rotating Kerr black holes connected by a massless strut, expanding understanding of binary black hole configurations in general relativity.

Contribution

It provides the first exact analytical metric for two Kerr black holes with specified parameters and explores the extremal limit within a known family of solutions.

Findings

Explicit metric for two Kerr black holes with arbitrary parameters

Connection to Kinnersly-Chitre family in the extremal limit

Complete characterization of the solution's parameters and limits

Abstract

The full metric describing two counter-rotating identical Kerr black holes separated by a massless strut is derived in the explicit analytical form. It contains three arbitrary parameters which are the Komar mass M, Komar angular momentum per unit mass a of one of the black holes (the other has the same mass and equal but opposite angular momentum) and the coordinate distance R between the centers of the horizons. In the limit of extreme black holes, the metric becomes a special member of the Kinnersly-Chitre five-parameter family of vacuum solutions generalizing the Tomimatsu-Sato delta=2 spacetime, and we present the complete set of metrical fields defining this limit.