Energy-momentum tensor for a Casimir apparatus in a weak gravitational field

TL;DR

This paper derives the energy-momentum tensor for a Casimir apparatus in a weak gravitational field, predicting a tiny upward push due to gravity, using a covariant perturbative approach.

Contribution

It provides a systematic derivation of the energy-momentum tensor for a Casimir setup in weak gravity, including gauge-invariant boundary conditions and conservation laws.

Findings

Casimir device experiences a tiny upward push in weak gravity

Derived energy-momentum tensor satisfies conservation and gauge conditions

Perturbative Green functions used for the analysis

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. We use Fermi coordinates and work to first order in the constant acceleration parameter. A perturbative expansion, to this order, of the Green functions involved and of the energy-momentum tensor is derived by means of the covariant geodesic point splitting procedure. In correspondence to the Green functions satisfying mixed and gauge-invariant boundary conditions, and Ward identities, the energy-momentum tensor is covariantly conserved and satisfies the expected relation between gauge-breaking and ghost parts. A more systematic derivation is therefore obtained of the theoretical prediction according to which the Casimir device in a weak gravitational field will experience a tiny push in the upwards direction.