Rotating charged black holes accelerated by an electric field

TL;DR

This paper generalizes Ernst's method for removing singularities in charged black hole metrics, establishing new equilibrium conditions for accelerated, rotating, and charged black holes under electric fields.

Contribution

It extends Ernst's approach to arbitrary accelerations and includes rotating black holes, providing new equilibrium conditions for these complex systems.

Findings

Generalized Ernst's equilibrium condition to arbitrary acceleration.

Removed nodal singularities in rotating charged black holes.

Derived new conditions for black hole acceleration and charge balance.

Abstract

The Ernst method of removing nodal singularities from the charged C-metric representing uniformly accelerated black holes with mass $m$, charge $q$ and acceleration $A$ by "adding" an electric field $E$ is generalized. Utilizing the new form of the C-metric found recently, Ernst's simple "equilibrium" condition $mA=qE$ valid for small accelerations is generalized for arbitrary $A$. The nodal singularity is removed also in the case of accelerating and rotating charged black holes, and the corresponding equilibrium condition is determined.