Casimir effect of electromagnetic field in Randall-Sundrum spacetime

TL;DR

This paper investigates the finite temperature Casimir effect for electromagnetic fields in Randall-Sundrum spacetime, comparing different boundary conditions and their impact on the Casimir force, revealing that corrections generally increase the force's attractiveness.

Contribution

It provides a detailed analysis of the Casimir effect in Randall-Sundrum spacetime without scalar field analogy, highlighting differences between 5D induced and 4D boundary conditions.

Findings

Both boundary conditions increase the Casimir force's attractiveness.

The 4D perfectly conducting condition yields smaller corrections than the 5D induced condition.

Corrections are consistent across all temperatures.

Abstract

We study the finite temperature Casimir effect on a pair of parallel perfectly conducting plates in Randall-Sundrum model without using scalar field analogy. Two different ways of interpreting perfectly conducting conditions are discussed. The conventional way that uses perfectly conducting condition induced from 5D leads to three discrete mode corrections. This is very different from the result obtained from imposing 4D perfectly conducting conditions on the 4D massless and massive vector fields obtained by decomposing the 5D electromagnetic field. The latter only contains two discrete mode corrections, but it has a continuum mode correction that depends on the thicknesses of the plates. It is shown that under both boundary conditions, the corrections to the Casimir force make the Casimir force more attractive. The correction under 4D perfectly conducting condition is always smaller than the correction under the 5D induced perfectly conducting condition. These statements are true at any temperature.