Properties of the distorted Kerr black hole

TL;DR

This paper explores how external gravitational fields distort Kerr black holes, affecting their ergoregions and singularities, with detailed analysis of quadrupole and octupole distortions and their impact on black hole properties.

Contribution

It provides a detailed study of the ergoregion and singularity behavior of distorted Kerr black holes, including new configurations and relationships with external distortions.

Findings

Ergoregion can be disconnected and extend to infinity.

Singularities are on the ergoregion boundary, not on the ergosurface.

External distortions affect the size and shape of the ergoregion.

Abstract

We investigate the properties of the ergoregion and the location of the curvature singularities for the Kerr black hole distorted by the gravitational field of external sources. The particular cases of quadrupole and octupole distortion are studied in detail. We also investigate the scalar curvature invariants of the horizon and compare their behaviour with the case of the isolated Kerr black hole. In a certain region of the parameter space the ergoregion consists of a compact region encompassing the horizon and a disconnected part extending to infinity. The curvature singularities in the domain of outer communication, when they exist, are always located on the boundary of the ergoregion. We present arguments that they do not lie on the compact ergosurface. For quadrupole distortion the compact ergoregion size is negatively correlated with the horizon angular momentum when the external sources are varied. For octupole distortion infinitely many ergoregion configurations can exist for a certain horizon angular momentum. For some special cases we can have $J^2/M^4 > 1$ and yet avoid the naked singularity.