Energy conditions for a generally coupled scalar field outside a reflecting sphere

TL;DR

This paper analyzes the energy conditions for a scalar field with general curvature coupling outside a reflecting sphere, demonstrating that the averaged null energy condition (ANEC) holds universally in this setup.

Contribution

It provides a detailed calculation of the stress-energy tensor for a coupled scalar field outside a reflecting sphere and shows the universality of the ANEC regardless of curvature coupling.

Findings

ANEC is obeyed for conformal coupling

ANEC is independent of curvature coupling in this scenario

The spherical case reduces to flat plate behavior near the boundary

Abstract

We calculate the stress-energy tensor 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 how the spherical case goes over to that of a flat plate as one approaches the sphere.