Quantum vacuum under mixed boundary conditions: the case for curved spacetime

TL;DR

This paper examines how gravity influences the quantum vacuum and Casimir energy for a scalar field under Robin boundary conditions in curved spacetime, revealing conditions that alter the vacuum energy and force.

Contribution

It provides a detailed calculation of the quantum vacuum energy in weak gravitational fields with Robin boundary conditions, including first-order perturbation corrections and parameter-specific energy independence.

Findings

Gravity generally decreases Casimir energy.

Certain parameters can increase the Casimir force.

Energy can be independent of Robin coefficients under specific conditions.

Abstract

Influence of gravity on the quantum vacuum of a massless minimally coupled scalar field under Robin boundary conditions on parallel plates is investigated. We introduce the detailed calculation of the volume energy for the case the gravitational background is weak in its most general form for a static spacetime. It founds that the quantum vacuum usually reacts to the gravitational field by decreasing the Casimir energy. In addition, we find sufficient conditions under which the Casimir force increases. Interestingly, the first order perturbation corrections, are present in the obtained formula for the volume energy. We show that for some specific choices of parameters, the energy is independent of Robin coefficients. Consistency with the literature is shown in some limiting cases and well-known examples are presented for both an increase or decrease in the volume energy.