Finite temperature Casimir effect for scalar field with Robin boundary conditions in spacetime with extra dimensions

TL;DR

This paper investigates the finite temperature Casimir effect for a scalar field with Robin boundary conditions in a higher-dimensional spacetime, analyzing force behaviors under various conditions and boundary parameters.

Contribution

It provides a detailed analysis of the Casimir force with Robin boundary conditions in extra-dimensional spacetime, including force sign transitions and asymptotic behaviors.

Findings

Casimir force can be attractive or repulsive depending on Robin coefficients.

Force behavior varies with plate separation and temperature.

Divergences cancel via the piston approach.

Abstract

In this article, we study the finite temperature Casimir effect for scalar field with Robin boundary conditions on two parallel plates in a background spacetime that has a compact internal manifold with arbitrary geometry. The finite temperature Casimir force acting on the plates is derived using the piston approach, with which we show that the divergences of the Casimir forces from the region between the plates and the region outside the plates cancel each other. The nature and asymptotic behaviors of the Casimir force at different limits such as small and large plate separation, low and high temperature, are studied in detail. The range of Robin coefficients where the Casimir force are always attractive or always repulsive are determined. There are also some range of the Robin coefficients where the Casimir force is shown to be attractive at small plate separation and repulsive at large plate separation, or vise versa.