Black holes in rotating, electromagnetic backgrounds and topological Kerr-Newman-NUT spacetimes

TL;DR

This paper classifies a broad family of stationary, axisymmetric black hole solutions in general relativity and Einstein-Maxwell theory based on their backgrounds, revealing a unified structure linked to the Kerr-Newman-NUT family and exploring new embeddings.

Contribution

It demonstrates that many known black hole solutions are special cases of the Kerr-Newman-NUT family within diverse topological backgrounds, including novel embeddings.

Findings

All these backgrounds are related to the double Wick rotation of topological Kerr-Newman-NUT metrics.

A new black hole solution embedded in a generalized rotating universe is presented.

Most known solutions are shown to belong to the Kerr-Newman-NUT family within specific backgrounds.

Abstract

We observe that a large class of well behaved stationary and axisymmetric black hole solutions in general relativity and in the Einstein-Maxwell theory can be classified according to the properties of their background. Indeed all these backgrounds belong to a unique family which includes simultaneously all the known axisymmetric and regular backgrounds: the swirling, the Bertotti-Robinson, the Bonnor-Melvin universe, Witten's expanding bubble and also other novel, regular, rotating gravitational or electromagnetic environments. All these can be, fundamentally, traced back to the double Wick rotation of the topological generalisation of (accelerating) Kerr-Newman-NUT metric. We present a black hole embedded in an unexplored sector of the general background: Schwarzschild inside a generalised rotating (and possibly electromagnetic) universe. These results indicate that basically all the known analytical and exact single black hole solutions in the four-dimensional Einstein-Maxwell theory belong to the (accelerating) Kerr-Newman-NUT family embedded into backgrounds that are a subcase of the conjugated Kerr-Newman-NUT space-time with an angular manifold of arbitrary topology.