Casimir effect for parallel metallic plates in cosmic string spacetime

TL;DR

This paper calculates the vacuum expectation values of electromagnetic fields and the Casimir forces between plates in a cosmic string spacetime, revealing how the string's presence influences quantum vacuum effects and forces.

Contribution

It provides a detailed analysis of electromagnetic vacuum fluctuations and Casimir forces in cosmic string backgrounds, including the decomposition into string and plate-induced parts.

Findings

Electric field squared VEV is negative near the string, positive farther away.

Magnetic field squared VEV is negative everywhere.

Casimir forces on plates are always attractive and depend on the string's distance.

Abstract

We evaluate the renormalized vacuum expectation values (VEVs) of electric and magnetic fields squared and the energy-momentum tensor for the electromagnetic field in the geometry of two parallel conducting plates on background of cosmic string spacetime. On the base of these results, the Casimir-Polder force 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 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 distance to the string smaller than the distance to the plates and negative in 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.