Metric of two balancing Kerr particles in physical parametrization

TL;DR

This paper develops a physical parametrization for the extended double-Kerr spacetime describing two spinning bodies in equilibrium, revealing stronger-than-expected spin-spin repulsion and linking it to other gravitational configurations.

Contribution

It provides a new analytical physical representation for the double-Kerr solution using Komar parameters, including special cases and relations to other solutions.

Findings

Existence of equilibrium configurations with superextreme objects.

Spin-spin repulsion can be stronger than previously thought.

Explicit formulas relate double-Kerr and double-Reissner-Nordström states.

Abstract

The present paper aims at elaborating a completely physical representation for the general 4-parameter family of the extended double-Kerr spacetimes describing two spinning sources in gravitational equilibrium. This involved problem is solved in a concise analytical form by using the individual Komar masses and angular momenta as arbitrary parameters, and the simplest equatorially symmetric specialization of the general expressions obtained by us yields the physical representation for the well-known Dietz-Hoenselaers superextreme case of two balancing identical Kerr constituents. The existence of the physically meaningful "black hole-superextreme object" equilibrium configurations permitted by the general solution may be considered as a clear indication that the spin-spin repulsion force might actually be by far stronger than expected earlier, when only the balance between two superextreme Kerr sources was thought possible. We also present the explicit analytical formulas relating the equilibrium states in the double-Kerr and double-Reissner-Nordstr\"om configurations.