From Rindler space to the electromagnetic energy-momentum tensor of a Casimir apparatus in a weak gravitational field

TL;DR

This paper calculates the electromagnetic energy-momentum tensor for a Casimir apparatus in a weak gravitational field, using a covariant approach based on Rindler spacetime, and improves previous first-order results by including second-order corrections.

Contribution

It introduces a fully covariant method to evaluate the electromagnetic energy-momentum tensor in a weak gravitational field, extending previous work by including second-order corrections in gravity acceleration g.

Findings

Components of the energy-momentum tensor are computed up to second order in g.

The analysis corrects and extends previous first-order formulas for Casimir energy.

The formalism is well-suited for arbitrary order calculations in weak gravitational fields.

Abstract

This paper studies two perfectly conducting parallel plates in the weak gravitational field on the surface of the Earth. Since the appropriate line element, to first order in the constant gravity acceleration g, is precisely of the Rindler type, we can exploit the formalism for studying Feynman Green functions in Rindler spacetime. Our analysis does not reduce the electromagnetic potential to the transverse part before quantization. It is instead fully covariant and well suited for obtaining all components of the regularized and renormalized energy-momentum tensor to arbitrary order in the gravity acceleration g. The general structure of the calculation is therefore elucidated, and the components of the Maxwell energy-momentum tensor are evaluated up to second order in g, improving a previous analysis by the authors and correcting their old first-order formula for the Casimir energy.