Local and global structure of domain wall space-times

TL;DR

This paper proves the equivalence of comoving and moving-wall approaches in domain wall space-times without reflection symmetry, providing a method to construct coordinates and analyze their global structure.

Contribution

It introduces a general proof of approach equivalence and a procedure for constructing comoving coordinates in complex domain wall space-times.

Findings

Derived gravitational fields for spherical, planar, and hyperbolic walls with M=0.

Solved Israel's junction conditions for these configurations.

Discussed the global structure of the resulting space-times.

Abstract

We present a general proof on the equivalence of the comoving-coordinate approach, where the wall is fixed at a constant coordinate variable, and moving-wall approach, where the wall is moving in a background static space-time, in the domain wall space-times without reflection symmetry. We further provide a general procedure to construct the comoving coordinates in the domain wall space-times, where the two regions separated by an infinite thin wall have different cosmological constant $\Lambda$ and Schwartzschild mass $M$. By solving Israel's junction conditions in the thin-wall limit, the gravitational fields of spherical, planar and hyperbolic domain wall space-times with M=0 in the two different comoving coordinate systems are obtained. We finally discuss the global structure of these domain wall space-times.