Null energy conditions outside a background potential

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.