Averaged null energy condition in spacetimes with boundaries

TL;DR

This paper proves that the Averaged Null Energy Condition (ANEC) cannot be violated by a quantized scalar field in flat spacetimes with boundaries, ensuring the stability of certain spacetime geometries.

Contribution

It demonstrates that under specific conditions, the ANEC holds in flat spacetimes with boundaries, extending its validity to scenarios like the Casimir effect.

Findings

ANEC holds in flat space with boundaries for geodesics away from the boundary.

Quantum scalar fields do not violate ANEC in the considered settings.

Supports the stability of spacetime geometries with boundaries against exotic phenomena.

Abstract

The Averaged Null Energy Condition (ANEC) requires that the average along a complete null geodesic of the projection of the stress-energy tensor onto the geodesic tangent vector can never be negative. It is sufficient to rule out many exotic phenomena in general relativity. Subject to certain conditions, we show that the ANEC can never be violated by a quantized minimally coupled free scalar field along a complete null geodesic surrounded by a tubular neighborhood in which the geometry is flat and whose intrinsic causal structure coincides with that induced from the full spacetime. In particular, the ANEC holds in flat space with boundaries, as in the Casimir effect, for geodesics which stay a finite distance away from the boundary