Casimir effect for parallel metallic plates in cosmic string spacetime

Abstract

We evaluate the renormalized vacuum expectation values (VEVs) of electric and magnetic field squared and the energy–momentum tensor for the electromagnetic field in the geometry of two parallel conducting plates on the background of cosmic string spacetime. On the basis of these results, the Casimir–Polder force acting on a polarizable particle and the Casimir forces acting on the plates are investigated. The VEVs are decomposed into the pure string and plate-induced parts. The VEV of the electric field squared is negative for points with the radial distance to the string smaller than the distance to the plates, and positive for the opposite situation. On the other hand, the VEV for the magnetic field squared is negative everywhere. The boundary-induced part in the VEV of the energy–momentum tensor is different from zero in the region between the plates only. Moreover, this part only depends on the distance from the string. The boundary-induced part in the vacuum energy density is positive for points with a distance to the string smaller than the distance to the plates and negative in the opposite situation. The Casimir stresses on the plates depend non-monotonically on the distance from the string. We show that the Casimir forces acting on the plates are always attractive.This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical in honour of Stuart Dowker's 75th birthday devoted to ‘Applications of zeta functions and other spectral functions in mathematics and physics’.