Spacetime Averaged Null Energy Condition

TL;DR

This paper investigates the averaged null energy condition in quantum fields within curved spacetime, demonstrating that even extended averaging procedures cannot universally enforce this condition due to specific counterexamples.

Contribution

It introduces a class of examples that violate any form of spacetime-averaged null energy condition, challenging assumptions about quantum energy inequalities.

Findings

Averaging over all dimensions does not guarantee the null energy condition

Counterexamples exist that violate any proposed averaged null energy condition

Quantum fields can violate energy conditions even with extensive averaging

Abstract

The averaged null energy condition has known violations for quantum fields in curved space, even if one considers only achronal geodesics. Many such examples involve rapid variation in the stress-energy tensor in the vicinity of the geodesic under consideration, giving rise to the possibility that averaging in additional dimensions would yield a principle universally obeyed by quantum fields. However, after discussing various procedures for additional averaging, including integrating over all dimensions of the manifold, we give a class of examples that violate any such averaged condition.