Weak Gravitational Field and Casimir Energy

Abstract

In this paper we consider the effect of a weak gravitation field on the Casimir energy. Under a weak perturbation of a metric, we first obtain the linear energy-momentum tensor of a scalar field in a generic background and then the corrected energy of a scalar filed which satisfies the Dirichlet boundary condition is calculated up to first order of the metric perturbation. We show that our results coincide to the previous related works e.g., the Casimir effect when studied in Fermi coordinates.