On Casimir Pistons

TL;DR

This paper investigates the Casimir force in a piston setup with one slightly curved dimension, revealing opposite force signs depending on piston movement, and explores semi-analytic methods and potential extra-dimensional effects.

Contribution

It introduces a detailed analysis of Casimir forces in curved piston configurations and compares different piston movements, including semi-analytic approaches and extra-dimensional considerations.

Findings

Casimir force sign depends on piston movement direction

Semi-analytic methods effectively analyze Casimir energy and force

Extra-dimensional modifications could influence Casimir effects

Abstract

In this paper we study the Casimir force for a piston configuration in $R^3$ with one dimension being slightly curved and the other two infinite. We work for two different cases with this setup. In the first, the piston is "free to move" along a transverse dimension to the curved one and in the other case the piston "moves" along the curved one. We find that the Casimir force has opposite signs in the two cases. We also use a semi-analytic method to study the Casimir energy and force. In addition we discuss some topics for the aforementioned piston configuration in $R^3$ and for possible modifications from extra dimensional manifolds.