Сharged black hole accelerated by spatially homogeneous electric field of Bertotti-Robinson (AdS${}^2\times \mathbb{S}^2$) space-time

The exact solution of Einstein - Maxwell field equations for charged non-rotating black hole accelerated by an external electric field is constructed as nonlinear superposition of electrovacuum fields using the monodromy transform approach to solution of integrable reductions of Einstein - Maxwell equations. The background space-time, described by the well known Bertotti-Robinson solution, contains a spatially homogeneous electric field and possess the topology AdS${}^2\times \mathbb{S}^2$. 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 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 and in the same background space-time.