Casimir effect in a weak gravitational field

Abstract

We study the Casimir vacuum energy density for a massless scalar field confined between two nearby parallel plates (a cavity) in a slightly curved, static spacetime background, employing the weak-field approximation. Following an order-by-order perturbative approach, we evaluate the gravity-induced correction to Casimir energy. We find evidence for a small shift in the (negative) vacuum energy. As a consequence, the (attractive) force between the cavity walls is expected to weaken. Although derived in the weak-field approximation, and too small to be detected with the current technology, such gravitationally induced shift in vacuum energy seems nevertheless interesting from a theoretical point of view, since it might play a role in a cosmological scenario (e.g., gravitational influence on the Λ-term) as well as at a microscopic level (quark confinement) in strong gravitational fields. Finally, the analysis of the possible gravitational effects on Casimir cavities faces the open issue concerning the limits of validity of general relativity at small distances.