The Casimir effect in the Fulling-Rindler vacuum

TL;DR

This paper analyzes the Casimir effect in the Fulling-Rindler vacuum for scalar and electromagnetic fields, revealing attractive forces between accelerated plates and addressing boundary condition effects in various dimensions.

Contribution

It provides a detailed calculation of vacuum expectation values and forces in the Fulling-Rindler vacuum for different fields and boundary conditions, including a regularization approach.

Findings

Interaction forces are always attractive for scalar and electromagnetic fields.

Mode-summation with Abel–Plana formula effectively isolates boundary contributions.

Surface divergences require additional regularization.

Abstract

The vacuum expectation values of the energy--momentum tensor are investigated for massless scalar fields satisfying Dicichlet or Neumann boundary conditions, and for the electromagnetic field with perfect conductor boundary conditions on two infinite parallel plates moving by uniform proper acceleration through the Fulling--Rindler vacuum. The scalar case is considered for general values of the curvature coupling parameter and in an arbitrary number of spacetime dimension. The mode--summation method is used with combination of a variant of the generalized Abel--Plana formula. This allows to extract manifestly the contributions to the expectation values due to a single boundary. The vacuum forces acting on the boundaries are presented as a sum of the self--action and interaction terms. The first one contains well known surface divergences and needs a further regularization. The interaction forces between the plates are always attractive for both scalar and electromagnetic cases. An application to the 'Rindler wall' is discussed.