Casimir Effect in Background of Static Domain Wall

TL;DR

This paper analyzes the Casimir effect for a conformally coupled scalar field in the presence of a static domain wall, combining boundary conditions and gravitational background effects to compute vacuum energy-momentum tensor values.

Contribution

It provides a method to calculate vacuum expectation values of energy-momentum tensor in a domain wall background using conformal properties and mode sums.

Findings

Results agree with previous Minkowski space calculations.

Vacuum energy-momentum tensor includes boundary and gravitational contributions.

Method applicable to similar boundary-gravity problems.

Abstract

In this paper we investigate the vacuum expectation values of energy- momentum tensor for conformally coupled scalar field in the standard parallel plate geometry with Dirichlet boundary conditions and on background of planar domain wall case. First we calculate the vacuum expectation values of energy-momentum tensor by using the mode sums, then we show that corresponding properties can be obtained by using the conformal properties of the problem. The vacuum expectation values of energy-momentum tensor contains two terms which come from the boundary conditions and the the gravitational background. In the Minkovskian limit our results agree with those obtained in [3].