Revisiting Vacuum Energy in Compact Spacetimes

TL;DR

This paper analyzes vacuum energy in compact spacetimes, examining how external electromagnetic fields influence Casimir forces and particle production rates, revealing magnetic fields reduce and electric fields increase the Casimir force.

Contribution

It provides new calculations of Casimir forces and particle production rates in compact spacetimes with external fields, extending previous analyses to more general configurations.

Findings

Magnetic fields decrease Casimir force strength.

Electric fields increase Casimir force strength.

Particle production rate is enhanced by the presence of a piston.

Abstract

We revisit the calculation of vacuum energy density in compact spacetimes. For the general case of $k$ compact spatial dimensions in $p+k$ dimensional Minkowski spacetime, we calculate the Casimir force on a piston placed in the presence of external electromagnetic fields. We observe that while the presence of a strong external magnetic field reduces the intensity of the Casimir force, the presence of an electric field enhances it instead. We discuss various physical cases, and also derive the particle production rate in the presence of such external fields in compact spacetimes. We observe that the pair production rate is enhanced in the presence of a piston.