Schwarzschild black hole levitating in the hyperextreme Kerr field

TL;DR

This paper analyzes equilibrium configurations where a Schwarzschild black hole is levitating in the gravitational and rotational field of a hyperextreme Kerr object, providing explicit solutions and physical interpretations.

Contribution

It introduces a specific three-parameter subfamily of the extended double-Kerr solution describing such equilibrium configurations with explicit metric functions and physical parameters.

Findings

Derived a simple expression for horizon's local angular velocity.

Identified a three-parameter family of solutions for black hole-Kerr configurations.

Provided a physical interpretation using Komar masses and separation distance.

Abstract

The equilibrium configurations between a Schwarzschild black hole and a hyperextreme Kerr object are shown to be described by a three-parameter subfamily of the extended double-Kerr solution. For this subfamily, its Ernst potential and corresponding metric functions, we provide a physical representation which employs as arbitrary parameters the individual Komar masses and relative coordinate distance between the sources. The calculation of horizon's local angular velocity induced in the Schwarzschild black hole by the Kerr constituent yields a simple expression inversely proportional to the square of the distance parameter.