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

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.