Metric for two arbitrary Kerr sources

TL;DR

This paper presents an explicit, concise metric for a stationary axisymmetric system of two Kerr sources, including special cases like a Schwarzschild black hole and a Kerr source, describing their equilibrium configuration.

Contribution

The authors derive a full explicit metric for two arbitrary Kerr sources in equilibrium, covering special cases such as a Schwarzschild black hole with a Kerr source.

Findings

Explicit metric involving five physical parameters

Includes special cases like Schwarzschild-Kerr system

Provides a concise formula for equilibrium configurations

Abstract

The full metric describing a stationary axisymmetric system of two arbitrary Kerr sources, black holes or hyperextreme objects, located on the symmetry axis and kept apart in equilibrium by a massless strut is presented in a concise explicit form involving five physical parameters. The binary system composed of a Schwarzschild black hole and a Kerr source is a special case not covered by the general formulas, and we elaborate the metric for this physically interesting configuration too.