Spherical Casimir pistons

TL;DR

This paper investigates the Casimir energy in spherical lune cavities with pistons, analyzing boundary conditions, temperature effects, and the resulting forces, revealing attraction or repulsion depending on dimensions and conditions.

Contribution

It introduces a piston into spherical lune Casimir cavities and analyzes the resulting vacuum energy and forces using zeta function regularization, including temperature effects and boundary conditions.

Findings

Vacuum energy is finite for conformal propagation in even spheres.

Pistons are attracted or repelled depending on boundary conditions and dimensions.

Finite temperature causes the free energy to develop two minima in certain cases.

Abstract

A piston is introduced into a spherical lune Casimir cavity turning it into two adjacent lunes separated by the (hemispherical) piston. On the basis of zeta function regularisation, the vacuum energy of the arrangement is finite for conformal propagation in space-time. For even spheres this energy is independent of the angle of the lune. For odd dimensions it is shown that for all Neumann, or all Dirichlet, boundary conditions the piston is attracted or repelled by the nearest wall if d=3,7,... or if d=1,5,..., respectively. For hybrid N-D conditions these requirements are switched. If a mass is added, divergences arise which render the model suspect. The analysis, however, is relatively straightforward and involves the Barnes zeta function. The extension to finite temperatures is made and it is shown that for the 3,7,... series of odd spheres, the repulsion by the walls continues but that, above a certain temperature, the free energy acquires two minima symmetrically placed about the mid point.