Accelerated Charge Kerr-Schild Metrics in D-Dimensions

TL;DR

This paper generalizes the Bonnor-Vaidya solution to D-dimensional Einstein-Maxwell theory with null fluid in Kerr-Schild geometry, deriving conditions for solutions and analyzing energy flux due to accelerated charged sources.

Contribution

It provides a complete set of differential conditions for solutions and explicitly constructs the metric, electromagnetic potential, and energy density in arbitrary D dimensions.

Findings

Generalization of Bonnor-Vaidya solution to D dimensions

Explicit energy flux formula for accelerated charged sources

Conditions for solutions in Einstein-Maxwell null fluid system

Abstract

We consider the D dimensional Einstein Maxwell theory with a null fluid in the Kerr-Schild Geometry. We obtain a complete set of differential conditions that are necessary for finding 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 $D \ge 4$ dimensions and we give the explicit form of this energy flux formula.