Kaluza-Klein models as pistons

TL;DR

This paper analyzes how extra dimensions in Kaluza-Klein models affect the Casimir force in pistons, showing a consistent tendency for the force to pull the center plate toward the nearer wall, regardless of geometry or temperature.

Contribution

It provides analytical expressions for the Casimir force in Kaluza-Klein pistons across different regimes and establishes the force's directional tendency independent of extra-dimensional details.

Findings

Casimir force tends to move the center plate toward the closer wall

Force behavior is consistent across different geometries and topologies

Finite temperature does not alter the main force tendency

Abstract

We consider the influence of extra dimensions on the force in Casimir pistons. Suitable analytical expressions are provided for the Casimir force in the range where the plate distance is small, and that where it is large, compared to the size of the extra dimensions. We show that the Casimir force tends to move the center plate toward the closer wall; this result is true independently of the cross-section of the piston and the geometry or topology of the additional Kaluza--Klein dimensions. The statement also remains true at finite temperature. In the limit where one wall of the piston is moved to infinity, the result for parallel plates is recovered. If only one chamber is considered, a criterion for the occurrence of Lukosz-type repulsion, as opposed to the occurrence of renormalization ambiguities, is given; we comment on why no repulsion has been noted in some previous cosmological calculations that consider only two plates.