Casimir effect in a weak gravitational field: Schwinger’s approach

Abstract

In this paper we discuss the Casimir effect in a small cavity at rest in the weak gravitational field of a massive, non-rotating source. We propose a new approach, based upon Schwinger’s effective action method, showing that the gravitational interaction induces a small correction in the vacuum energy density, in full agreement with the result we obtained in a previous work (Sorge 2005 Class. Quantum Grav. 22 5109), following a standard field mode decomposition technique. The present result reinforces the belief that gravity can indeed be effective in modifying the vacuum energy of a quantum field confined to the cavity, against the recent claim appeared in Lima et al (2019 J. Cosmol. Astropart. Phys. JCAP07(2019)11) that a weak gravitational field has no influence on the Casimir energy.