Scalar Casimir effect between two concentric D-dimensional spheres

TL;DR

This paper calculates the Casimir energy for a massless scalar field between two closely spaced concentric D-dimensional spheres, revealing a strictly negative energy under Dirichlet boundary conditions, which has implications for stability analysis.

Contribution

It provides a novel calculation of the Casimir energy in higher-dimensional spherical geometries using mode summation and complex analysis techniques.

Findings

Casimir energy is strictly negative for the configuration.

Method employs contour integration and Abel-Plana formula.

Results are relevant for stability considerations of the force.

Abstract

The Casimir energy for a massless scalar field between the closely spaced two concentric D-dimensional (for D>3) spheres is calculated by using the mode summation with contour integration in the complex plane of eigenfrequencies and the generalized Abel-Plana formula for evenly spaced eigenfrequency at large argument. The sign of the Casimir energy between closely spaced two concentric D-dimensional spheres for a massless scalar field satisfying the Dirichlet boundary conditions is strictly negative. The Casimir energy between D-1 dimensional surfaces close to each other is regarded as interesting both by itself and as the key to describing of stability of the attractive Casimir force. PACS number(s): 03.70.+k, 11.10.Kk, 11.10.Gh, 03.65.Ge