Casimir effect in a weak gravitational field and the spacetime index of refraction

TL;DR

This paper calculates how a weak static gravitational field influences the vacuum energy in a Casimir setup using quantum field theory in curved spacetime, supporting a conjecture relating gravity to spacetime's index of refraction.

Contribution

It explicitly computes the effect of gravity on virtual scalar particles in a Casimir apparatus, providing evidence for a conjecture linking gravitational influence to spacetime's index of refraction.

Findings

Gravitational field affects the frequency and energy of virtual scalar particles.

Results support the conjecture relating gravitational effects to spacetime's index of refraction.

Discusses extensions to stationary spacetimes and virtual photons.

Abstract

In a recent paper [arXiv:0904.2904] using a conjecture it is shown how one can calculate the effect of a weak stationary gravitational field on vacuum energy in the context of Casimir effect in an external gravitational field treated in 1+3 formulation of spacetime decomposition.. In this article, employing quntum field theory in curved spacetime, we explicitly calculate the effect of a weak static gravitational field on virtual massless scalar particles in a Casimir apparatus. It is shown that, as expected from the proposed conjecture, both the frequency and renormalized energy of the virtual scalar field are affected by the gravitational field through its index of refraction. This could be taken as a strong evidence in favour of the proposed conjecture. Generalizations to weak {\it stationary} spacetimes and virtual photons are also discussed.