Accelerated charge Kerr-Schild metrics in D dimensions

Abstract

We consider the D-dimensional Einstein-Maxwell theory with a null fluid in Kerr-Schild geometry. We obtain a complete set of differential conditions that are necessary for finding the solutions. We examine the case of vanishing pressure and cosmological constant in detail. For this specific case, we give the metric, the electromagnetic vector potential and the fluid energy density. This is, in fact, the generalization of the well-known Bonnor-Vaidya solution to arbitrary D dimensions. We show that due to the acceleration of charged sources, there is an energy flux in D ≥ 4 dimensions and we give the explicit form of this energy flux formula.