Kerr black hole in a uniform Bertotti-Robinson magnetic field: An exact solution

TL;DR

This paper introduces a new exact solution describing Kerr black holes immersed in a uniform external magnetic or electric field, expanding the understanding of black hole environments in Einstein-Maxwell theory.

Contribution

It presents a novel class of axisymmetric stationary solutions to Einstein-Maxwell equations with non-aligned Maxwell fields, generalizing previous models like Kerr-Melvin and Bertotti-Robinson.

Findings

New exact Kerr black hole solutions in uniform magnetic fields.

Solutions reduce to Kerr or Bertotti-Robinson in special limits.

Potential applications in astrophysics and mathematical relativity.

Abstract

A new class of exact spacetimes in Einstein's gravity, which are Kerr black holes immersed in an external magnetic (or electric) field that is asymptotically uniform and oriented along the rotational axis, is presented. These are axisymmetric stationary solutions to the Einstein-Maxwell equations such that (unlike in the Plebanski-Demianski spacetime) the null directions of the Faraday tensor are not aligned with neither of the two principal null directions of the Weyl tensor of algebraic type D (unlike the Kerr-Melvin spacetime). Three physical parameters are the black hole mass $m$, its rotation $a$, and the external field value $B$. For vanishing $B$ the metric directly reduces to standard Boyer-Lindquist form of the Kerr black hole, while for zero $m$ we recover conformally flat Bertotti-Robinson universe with a uniform Maxwell field. For zero $a$ the spacetime is contained in the Van den Bergh-Carminati solutions which can be understood as the Schwarzschild black hole in a magnetic field. Our family of black holes with non-aligned Maxwell hair - that can be called the Kerr-Bertotti-Robinson (Kerr-BR) black holes - may find application in various studies ranging from mathematical relativity to relativistic astrophysics.