Casimir effect of two conducting parallel plates in a general weak gravitational field

TL;DR

This paper calculates the vacuum energy density of scalar and electromagnetic fields between parallel plates in a weak gravitational field, providing exact solutions and general formulas applicable to various weak backgrounds.

Contribution

It derives exact mode frequencies and energy densities for fields in a weak gravitational field, extending Casimir effect analysis to curved spacetime scenarios.

Findings

Mode frequencies are obtained exactly in Fermi spacetime.

Energy density formulas are generalized for weak gravitational backgrounds.

Results are consistent with existing literature on weak gravitational effects.

Abstract

We calculate the finite vacuum energy density of the scalar and electromagnetic fields inside a Casimir apparatus made up of two conducting parallel plates in a general weak gravitational field. The metric of the weak gravitational field has a small deviation from flat spacetime inside the apparatus and we find it by expanding the metric in terms of small parameters of the weak background. We show that the found metric can be transformed via a gauge transformation to the Fermi metric. We solve the Klein-Gordon equation exactly and find mode frequencies in Fermi spacetime. Using the fact that the electromagnetic field can be represented by two scalar fields in the Fermi spacetime, we find general formulas for the energy density and mode frequencies of the electromagnetic field. Some well-known weak backgrounds are examined and consistency of the results with the literature is shown.