Domain wall space-times with a cosmological constant

TL;DR

This paper derives exact solutions to Einstein's equations with a cosmological constant for space-times with domain walls, revealing new solutions like a conformally flat planar domain wall in de Sitter space.

Contribution

It provides the first comprehensive set of solutions for domain wall space-times with a cosmological constant, including a novel conformally flat planar domain wall in de Sitter universe.

Findings

Exact solutions in null coordinates for domain wall space-times.

A constraint equation from Israel's junction conditions.

Discovery of a conformally flat planar domain wall in de Sitter space.

Abstract

We solve vacuum Einstein's field equations with the cosmological constant in space-times admitting 3-parameter group of isometries with 2-dimensional space-like orbits. The general exact solutions, which are represented in the advanced and retarded null coordinates, have two arbitrary functions due to the freedom of choosing null coordinates. In the thin-wall approximation, the Israel's junction conditions yield one constraint equation on these two functions in spherical, planar, and hyperbolic domain wall space-times with reflection symmetry. The remain freedom of choosing coordinates are completely fixed by requiring that when surface energy density $\sigma_0$ of domain walls vanishes, the metric solutions will return to some well-known solutions. It leads us to find a planar domain wall solution, which is conformally flat, in the de Sitter universe.