Se p 20 05 Energy conditions for a generally coupled scalar field outside a reflecting sphere

Abstract We analyze the stress-energy tensor, and the resulting energy conditions, for a scalar field with general curvature coupling, outside a perfectly reflecting sphere with Dirichlet boundary conditions. For conformal coupling we find that the null energy condition is always obeyed, and therefore the averaged null energy condition (ANEC) is also obeyed. Since the ANEC is independent of curvature coupling, we conclude that the ANEC is obeyed for scalar fields with any curvature coupling in this situation. We also show explicitly how the spherical case goes over to that of a flat plate as one approaches the sphere.