Black holes in the external Bertotti-Robinson-Bonnor-Melvin electromagnetic field

TL;DR

This paper constructs an exact solution in general relativity describing a Schwarzschild-like black hole in a complex external electromagnetic field, analyzing its properties and limits.

Contribution

It introduces a new analytical spacetime solution combining multiple electromagnetic fields around a black hole, expanding understanding of such configurations.

Findings

Derived a new exact solution using Harrison transformation.

Analyzed conserved charges and thermodynamics of the black hole.

Explored limits to known solutions like Schwarzschild-Bertotti-Robinson.

Abstract

An exact and analytical solution, in four-dimensional general relativity coupled with Maxwell electromagnetism, is built by means of a Lie point symmetry of the Ernst equations, the Harrison transformation. The new spacetime describes a Schwarzschild-like black hole embedded into a general external back-reacting electromagnetic field, which is the superposition of the Levi-Civita-Bertotti-Robinson and the Bonnor-Melvin ones. The relation between the two homogeneous electromagnetic fields is clarified. Conserved charges and the first law of thermodynamics are analysed. Swirling generalisations are also considered. Limits to the known metrics such as Schwarzschild-Bertotti-Robinson, Schwarzschild-Bonnor-Melvin and Bertotti-Robinson-Bonnor-Melvin are discussed.