Null energy conditions outside a background potential

TL;DR

This paper investigates the null energy condition violations in the Casimir energy of a massless scalar field around spherical potentials, providing general formulas and specific cases in different dimensions.

Contribution

It derives a general expression for the null energy condition in arbitrary dimensions and analyzes specific spherical boundary cases in 3+1 and 2+1 dimensions.

Findings

Null energy condition is violated for radial motion.

Null energy condition is obeyed for azimuthal motion.

The averaged null energy condition always holds.

Abstract

We study the Casimir energy of a minimally coupled, real, massless scalar field outside a spherically symmetric background potential. We obtain a general expression for the null energy condition in d dimensions and explicit expressions for a perfectly reflecting spherical boundary in 3+1 and 2+1 dimensions. In these cases, the null energy condition is always violated for radial motion and obeyed for azimuthal motion. Nevertheless, the averaged null energy condition is always obeyed.