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-Nordström 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.

Typos corrected, 20 pages, no figures

References in corpus (5)

• Non-relativistic holography
• Black holes in asymptotically Lifshitz spacetime
• Gravitational Perturbations of Higher Dimensional Rotating Black Holes: Tensor Perturbations
• The Geroch group in Einstein spaces
• Anti-de Sitter massless scalar field spacetimes in arbitrary dimensions

Cited by in corpus (5)

• Electric/magnetic universe with a cosmological constant
• Higher-dimensional Buchdahl and Janis-Robinson-Winicour transformations in the Einstein-Maxwell system with a massless scalar field
• Solenoid configurations and gravitational free energy of the AdS--Melvin spacetime
• Kasner-type singularities and solitons with Lifshitz asymptotics
• Weyl-type solutions with multipolar scalar fields