Casimir interactions of an object inside a spherical metal shell

TL;DR

This paper analyzes the electromagnetic Casimir forces and torques on objects inside a spherical metal shell, providing analytical and numerical results that extend understanding of Casimir interactions in confined geometries.

Contribution

It offers analytical calculations for small objects and numerical corrections for sphere-shaped objects inside a spherical shell, bridging interior and exterior Casimir configurations.

Findings

Force directed away from the cavity center

Torque tends to align objects opposite to external alignment

Results match smoothly between interior and exterior configurations

Abstract

We investigate the electromagnetic Casimir interactions of an object contained within an otherwise empty, perfectly conducting spherical shell. For a small object we present analytical calculations of the force, which is directed away from the center of the cavity, and the torque, which tends to align the object opposite to the preferred alignment outside the cavity. For a perfectly conducting sphere as the interior object, we compute the corrections to the proximity force approximation (PFA) numerically. In both cases the results for the interior configuration match smoothly onto those for the corresponding exterior configuration.