Push on a Casimir apparatus in a weak gravitational field

TL;DR

This paper investigates how a weak gravitational field affects the Casimir effect, deriving a formula that predicts a tiny upward push on the apparatus due to gravity's influence on quantum electromagnetic fields.

Contribution

It provides a first-order derivation of the energy-momentum tensor in a gravitational field and introduces a new simple formula for the trace anomaly in this context.

Findings

Derivation of the energy-momentum tensor in a weak gravitational field

A new simple formula for the trace anomaly

Prediction of a tiny upward push on the Casimir apparatus

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 new simple formula for the trace anomaly is found to first order in the constant acceleration, and 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.