Cohomogeneity-1 solutions in Einstein-Maxwell-dilaton gravity

Abstract

The field equations for Einstein-Maxwell-dilaton gravity in $D$ dimensions are reduced to an effective one-dimensional system under the influence of exponential potentials. Various cases where exact solutions can be found are explored. With this procedure, we present interesting solutions such as a one-parameter generalisation of the dilaton-Melvin spacetime and a three-parameter solution that interpolates between the Reissner-Nordstr\"{o}m and Bertotti-Robinson solution. This procedure also allows simple, alternative derivations of known solutions such as the Lifshitz spacetime and the planar Anti-de Sitter naked singularity. In the latter case, the metric is cast in a simpler form which reveals the presence of an additional curvature singularity.