Thick domain wall spacetimes with and without reflection symmetry

TL;DR

This paper classifies thick domain wall spacetimes based on reflection symmetry, revealing that symmetric walls are dynamic and asymmetric ones are static, with diverse asymptotic behaviors and new solution families.

Contribution

It introduces a classification of domain wall solutions into symmetric and asymmetric types, extending thin-wall limit results and presenting new static solutions including BPS walls.

Findings

Symmetric walls are dynamic; asymmetric walls are static.

Asymmetric walls are asymptotically flat on one side and Taub on the other.

New families of solutions, including BPS walls, are identified.

Abstract

We show that the spacetimes of domain wall solutions to the coupled Einstein-scalar field equations with a given scalar field potential fall into two classes, depending on whether or not reflection symmetry on the wall is imposed. Solutions with reflection symmetry are dynamic, while the asymmetric ones are static. Asymmetric walls are asymptotically flat on one side and reduce to the Taub spacetime on the other. Examples of asymmetric thick walls in D-dimensional spacetimes are given, and results on the thin-wall limit of the dynamic, symmetric walls are extended to the asymmetric case. The particular case of symmetric, static spacetimes is considered and a new family of solutions, including previously known BPS walls, is presented.