Einstein-Maxwell-Dilaton theories with a Liouville potential

TL;DR

This paper explores solutions to Einstein-Maxwell-Dilaton theories with a Liouville potential across various dimensions, providing analytical and numerical solutions including black holes and solitons, and introduces a solution-generating technique similar to EM duality.

Contribution

It derives a unified approach to solving Einstein-Maxwell-Dilaton equations with Liouville potential, including explicit solutions and a novel solution-generating method.

Findings

Explicit black hole and soliton solutions in four and higher dimensions.

Reduction of field equations to manageable ODEs for various symmetries.

A new solution-generating technique akin to electromagnetic duality.

Abstract

We find and analyse solutions of Einstein's equations in arbitrary d dimensions and in the presence of a scalar field with a Liouville potential coupled to a Maxwell field. We consider spacetimes of cylindrical symmetry or again subspaces of dimension d-2 with constant curvature and analyse in detail the field equations and manifest their symmetries. The field equations of the full system are shown to reduce to a single or couple of ODE's which can be used to solve analytically or numerically the theory for the symmetry at hand. Further solutions can also be generated by a solution generating technique akin to the EM duality in the absence of a cosmological constant. We then find and analyse explicit solutions including black holes and gravitating solitons for the case of four dimensional relativity and the higher-dimensional oxydised 5-dimensional spacetime. The general solution is obtained for a certain relation between couplings in the case of cylindrical symmetry.