Finite Temperature Casimir Effect in Kaluza-Klein Spacetime

TL;DR

This paper investigates the finite temperature Casimir effect in Kaluza-Klein spacetime with arbitrary internal geometries, showing the force is always attractive and depends on the size of extra dimensions, with detailed temperature behavior.

Contribution

It provides a comprehensive analysis of the Casimir force at finite temperature in Kaluza-Klein models with general internal spaces, including asymptotic behaviors and force magnitude dependence.

Findings

Casimir force is always attractive regardless of internal space geometry.

Force magnitude increases with internal space size and temperature.

High temperature regime shows linear growth of force with temperature.

Abstract

In this article, we consider the finite temperature Casimir effect in Kaluza-Klein spacetime due the the vacuum fluctuation of massless scalar field with Dirichlet boundary conditions. We consider the general case where the extra dimensions (internal space) can be any compact connected manifold or orbifold without boundaries. Using piston analysis, we show that the Casimir force is always attractive at any temperature, regardless of the geometry of the internal space. Moreover, the magnitude of the Casimir force increases as the size of the internal space increases and it reduces to the Casimir force in (3+1)-dimensional Minskowski spacetime when the size of the internal space shrinks to zero. In the other extreme where the internal space is large, the Casimir force can increase beyond all bound. Asymptotic behaviors of the Casimir force in the low and high temperature regimes are derived and it is observed that the magnitude of the Casimir force grows linearly with temperature in the high temperature regime.