The Casimir force on a piston in the spacetime with extra compactified dimensions

TL;DR

This paper derives exact formulas for the Casimir force on a piston in high-dimensional spacetimes with extra compactified dimensions, revealing how additional dimensions influence the force's magnitude and behavior.

Contribution

It provides a detailed analysis of the Casimir force in high-dimensional Kaluza-Klein spacetimes, including exact expressions and limiting behaviors, which was not previously established.

Findings

The Casimir force becomes stronger with more extra dimensions.

In the limit of distant plates, the force reduces to the standard 4D form.

The force remains attractive regardless of extra dimensions.

Abstract

A one-dimensional Casimir piston for massless scalar fields obeying Dirichlet boundary conditions in high-dimensional spacetimes within the frame of Kaluza-Klein theory is analyzed. We derive and calculate the exact expression for the Casimir force on the piston. We also compute the Casimir force in the limit that one outer plate is moved to the extremely distant place to show that the reduced force is associated with the properties of additional spatial dimensions. The more dimensionality the spacetime has, the stronger the extra-dimension influence is. The Casimir force for the piston in the model excluding one plate under the background with extra compactified dimensions always keeps attractive. Further we find that when the limit is taken the Casimir force between one plate and the piston will change to be the same form as the corresponding force for the standard system consisting of two parallel plates in the four-dimensional spacetimes if the ratio of the plate-piston distance and extra dimensions size is large enough.