Plane symmetric gravitational fields in (D+1)-dimensional General Relativity

TL;DR

This paper explores higher-dimensional plane symmetric gravitational fields in General Relativity, presenting new solutions with cosmological constants, and analyzing boundary matching conditions and surface energy-momentum tensors.

Contribution

It introduces higher-dimensional generalizations of Rindler and Taub spacetimes with cosmological constants and studies boundary matching conditions.

Findings

Derived new vacuum solutions in higher dimensions.

Analyzed boundary matching with surface energy-momentum tensors.

Presented examples involving Rindler, Taub, and Minkowski spacetimes.

Abstract

We consider plane symmetric gravitational fields within the framework of General Relativity in (D+1)-dimensional spacetime. Two classes of vacuum solutions correspond to higher-dimensional generalizations of the Rindler and Taub spacetimes. The general solutions are presented for a positive and negative cosmological constant as the only source of the gravity. Matching conditions on a planar boundary between two regions with distinct plane symmetric metric tensors are discussed. An example is considered with Rindler and Taub geometries in neighboring half-spaces. As another example, we discuss a finite thickness cosmological constant slab embedded into the Minkowski, Rindler and Taub spacetimes. The corresponding surface energy-momentum tensor is found required for matching the exterior and interior geometries.