Averaged null energy condition in a classical curved background

TL;DR

This paper proves that the Averaged Null Energy Condition (ANEC) holds for a quantum scalar field in curved spacetimes with small curvature, supporting the stability of classical energy conditions in such backgrounds.

Contribution

It demonstrates that ANEC is obeyed in curved backgrounds with small curvature, extending flat-space quantum inequalities to more general classical spacetimes.

Findings

ANEC holds for quantum scalar fields in curved backgrounds with small curvature.

Exotic spacetimes require ANEC violation, which this work supports does not occur under specified conditions.

Supports the stability of classical energy conditions in curved spacetime contexts.

Abstract

The Averaged Null Energy Condition (ANEC) states that the integral along a complete null geodesic of the projection of the stress-energy tensor onto the tangent vector to the geodesic cannot be negative. Exotic spacetimes, such as those allow wormholes or the construction of time machines are possible in general relativity only if ANEC is violated along achronal geodesics. Starting from a conjecture that flat-space quantum inequalities apply with small corrections in spacetimes with small curvature, we prove that ANEC is obeyed by a minimally-coupled, free quantum scalar field on any achronal null geodesic surrounded by a tubular neighborhood whose curvature is produced by a classical source.