Casimir densities for parallel plate in the Domain Wall background

TL;DR

This paper investigates the Casimir effect for parallel plates in a domain wall background, deriving formulas for vacuum energy and forces for a conformally coupled scalar field with mixed boundary conditions.

Contribution

It provides new analytical expressions for vacuum expectation values and forces in a conformally flat domain wall background with mixed boundary conditions.

Findings

Formulas for vacuum energy-momentum tensor are derived.

Vacuum forces on plates are calculated.

Results apply to conformally coupled massless scalar fields in this setting.

Abstract

The Casimir forces on two parallel plates in conformally flat domain wall background due to conformally coupled massless scalar field satisfying mixed boundary conditions on the plates is investigated. In the general case of mixed boundary conditions formulae are derived for the vacuum expectation values of the energy-momentum tensor and vacuum forces acting on boundaries.