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 generalization of the dilaton-Melvin spacetime and a three-parameter solution that interpolates between the Reissner-Nordström and Bertotti-Robinson solutions. 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.

• Received 21 February 2017

DOI:https://doi.org/10.1103/PhysRevD.95.104008