Novel features of the energy momentum tensor of a Casimir apparatus in a weak gravitational field

TL;DR

This paper investigates how a weak gravitational field affects the energy-momentum tensor of the electromagnetic field in a Casimir setup, revealing new features through a perturbative analysis.

Contribution

It provides a first-order perturbative derivation of the energy-momentum tensor in a gravitational field, highlighting novel features of the Casimir energy in such conditions.

Findings

Energy-momentum tensor is covariantly conserved.

The tensor satisfies the expected gauge and ghost relations.

First-order gravitational effects on Casimir energy are characterized.

Abstract

The influence of the gravity acceleration on the regularized energy-momentum tensor of the quantized electromagnetic field between two plane parallel conducting plates is derived. A perturbative expansion, to first order in the constant acceleration parameter, of the Green functions involved and of the energy-momentum tensor is derived by means of the covariant geodesic point splitting procedure. The energy-momentum tensor is covariantly conserved and satisfies the expected relation between gauge-breaking and ghost parts.