Dilaton spacetimes with a Liouville potential

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 ten-dimensional string theories, the open USp(32) type I string and the heterotic string SO(16) × SO(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 behaviour 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 analyse 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.