Charged black hole accelerated by spatially homogeneous electric field of Bertotti-Robinson (AdS2 x S2) space-time

TL;DR

This paper presents an exact solution describing a charged, non-rotating black hole accelerated by a uniform electric field within the Bertotti-Robinson spacetime, revealing insights into black hole dynamics in such electromagnetic backgrounds.

Contribution

It introduces a new exact Einstein-Maxwell solution for a charged black hole in a homogeneous electric field within AdS2 x S2 space, detailing its properties and acceleration conditions.

Findings

Black hole acceleration determined by conical singularity conditions

Solution is static in a comoving non-inertial frame

Comparison with charged test particle behavior

Abstract

A simple exact solution of the Einstein - Maxwell field equations for charged non-rotating black hole accelerated by an external electric field is presented. The background space-time, described by the well known Bertotti-Robinson solution, contains a spatially homogeneous electric field and possess the topology AdS2 x S2. The black hole mass m, its charge e and the value of the background electric field E are free parameters of the constructed solution. In the "rigid" (non-inertial) reference frame comoving a black hole, this solution is static. The value of acceleration of a black hole due to its interaction with the external electric field is determined by the condition of vanishing of conical singularities on the axis of symmetry. The dynamics of a charged black hole in the external electric field is compared with the behaviour of a charged test particle with the same charge to mass ratio.