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

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.

Relativistic mechanics of Casimir apparatuses in a weak gravitational field

“…The formula for the push has been obtained in three different ways, i.e. a heuristic summation over modes [16,17], or a variational approach [7,8], or an energy-momentum analysis [9,15]. Moreover, the work in Ref.…”

“…The work in Ref. [15] has instead exploited the fact that, to first order in the small quantity gz, the line element (1.1) coincides with the Rindler metric…”

Casimir energy for two and three superconducting coupled cavities: Numerical calculations

“…The ARCHIMEDES experiment [1] is designed for testing whether the energy of vacuum fluctuations, foreseen by quantum electrodynamics, contributes to gravity, through the coupling demanded by quantum field theory in curved spacetime [2][3][4][5], where the Einstein tensor is taken to be proportional to the expectation value of the regularized and renormalized energy-momentum tensor of matter fields. The idea is to weigh the vacuum energy stored in a rigid Casimir cavity made by parallel conducting plates, by modulating the reflectivity of the plates upon inducing a transition from the metallic to the superconducting phase [1].…”

Energy-momentum tensor for a scalar Casimir apparatus in a weak gravitational field: Neumann conditions

“…Quantum field theory in curved spacetime, although far from being a definitive theory unifying the quantum theories with gravitation, offers nevertheless some intriguing results, such as the well-known Hawking radiation [1] and the closely related Unruh effect [2]. Moreover, in the recent literature, a number of papers studying the influence of a gravitational field on the energy stored in a Casimir cavity appeared [3,4,5,6], in particular nowadays the theoretical prediction that the vacuum fluctuations follow the equivalence principle seems to be demonstrated [4,5,7,8].…”