Dilaton spacetimes with a Liouville potential

TL;DR

This paper derives and analyzes a broad class of D-dimensional dilaton spacetimes with Liouville potentials, revealing their properties, singularities, and applications in string theory backgrounds, including cosmological and brane-world models.

Contribution

It provides the first comprehensive set of solutions for Einstein-scalar systems with Liouville potentials under planar symmetry, including static and dynamic cases, and explores their string theory relevance.

Findings

Static solutions are generally singular, sometimes with horizons.

Time-dependent solutions can avoid singularities, resembling thick domain walls.

The solutions demonstrate the breakdown of Birkhoff's theorem with scalar matter.

Abstract

We find and study solutions to the Einstein equations in D dimensions coupled to a scalar field source with a Liouville potential under the assumption of D-2 planar symmetry. The general static or time-dependent solutions are found yielding three classes of SO(D-2) symmetric spacetimes. In D=4 homogeneous and isotropic subsets of these solutions yield planar scalar field cosmologies. In D=5 they represent the general static or time-dependent backgrounds for a dilatonic wall-type brane Universe of planar cosmological symmetry. Here we apply these solutions as SO(8) symmetric backgrounds to non-supersymmetric 10 dimensional string theories, the open USp(32) type I string and the heterotic string SO(16)XSO(16). We obtain the general SO(9) solutions as a particular case. All static solutions are found to be singular with the singularity sometimes hidden by a horizon. The solutions are not asymptotically flat or of constant curvature. The singular behavior is no longer true once we permit space and time dependence of the spacetime metric much like thick domain wall or global vortex spacetimes. We analyze the general time and space dependent solutions giving implicitly a class of time and space dependent solutions and describe the breakdown of an extension to Birkhoff's theorem in the presence of scalar matter. We argue that the solutions described constitute the general solution to the field configuration under D-2 planar symmetry.