Motion of a weakly charged rotating black hole in a homogeneous electromagnetic field

TL;DR

This paper derives exact solutions describing the interaction of a weakly charged, rotating black hole with a homogeneous electromagnetic field, analyzing the resulting forces, torques, and changes in the black hole's properties.

Contribution

It provides new exact solutions for a charged rotating black hole in an external electromagnetic field and analyzes its dynamics and fluxes without altering the spacetime geometry.

Findings

Calculated electromagnetic fluxes into the black hole.

Derived equations for mass and spin evolution.

Analyzed effects of charge and spin on black hole motion.

Abstract

In this paper we consider a rotating black hole with electric and magnetic monopole charges that moves in a static homogeneous electromagnetic field. We assume that both the charges and the fields are weak, so that they have no effect on the spacetime geometry, which is described by the Kerr metric. We present exact solutions to Maxwell's equations describing the field of a charged rotating black hole moving in an external field background. We use these solutions to calculate the energy, momentum, and angular momentum fluxes of the electromagnetic field into the black hole. Using these results, we obtain expressions for the torque and force acting on the moving charged rotating black hole arising as a result of its interaction with the external electromagnetic field. We calculate these quantities both in the frame comoving with the black hole and in the frame of the external background field. We use this result to derive the equations that govern the change in the black hole's mass and spin, as well as the motion of the black hole. We provide exact solutions for specific cases which illustrate the role of charge and spin on the motion of the black hole.