Gravitational field of domain wall in Lyra geometry

TL;DR

This paper derives exact solutions for the gravitational field of a domain wall in Lyra geometry, revealing that the surrounding hypersurfaces are de Sitter spaces and that the gravitational influence is attractive.

Contribution

It introduces exact solutions for domain walls in Lyra geometry with time-dependent displacement vectors, expanding understanding of their gravitational properties.

Findings

Hypersurfaces parallel to the wall are de Sitter spaces.

The gravitational field of the domain wall is attractive.

Exact solutions for scalar fields with potential in Lyra geometry are obtained.

Abstract

In this paper, we study the domain wall with time dependent displacement vectors based on Lyra geometry in normal gauge i.e. displacement vector $f^*_i = [ \beta (t), 0,0,0]$. The field theoretic energy momentum tensor is considered with zero pressure perpendicular to the wall. We find an exact solutions of Einstein equation for a scalar field $\phi$ with a potential $V(\phi)$ describing the gravitational field of a plane symmetric domain wall. We have seen that the hyper surfaces parallel to the wall ($ z = constant $) are three dimensional de-sitter spaces. It is also shown that the gravitational field experienced by test particle is attractive.