Homogeneous Solutions of the Einstein-Maxwell Equations

Abstract

In this paper the solutions of the Einstein-Maxwell equations are investigated under the assumption that the metric of the space-time and the electromagnetic field are invariant under the transformations of a four-parametric, simply transitive group. The results can be summarized as follows: In the case of null electromagnetic fields there are two different possibilities; If Λ = 0, all the solutions are Robinson waves; if Λ ≠ 0, there exists only one solution, first given here by (6.26). There exist no other solutions for null electromagnetic fields. In the case of nonnull electromagnetic fields two solutions are found. One metric is known having been first given by Robinson; we give a new solution of type I. The question as to whether there are solutions different from these remains open.