Achronal averaged null energy condition
Noah Graham, Ken D. Olum
TL;DR
The paper proposes a weaker, self-consistent achronal averaged null energy condition (Condition 1) that requires ANEC to hold only on complete, achronal null geodesics while using the full stress-energy in semiclassical gravity. This refinement avoids known quantum violations and, within the semiclassical regime, suffices to reproduce key GR results such as topological censorship, the nonexistence of closed timelike curves, and certain positive-mass and singularity theorems, by ensuring that problematic geodesics (achronal complete null geodesics) cannot occur. The work argues that scale anomalies do not produce self-consistent violations under this framework, though caveats remain for half-geodesic analyses and Casimir-type configurations, indicating the need for additional constraints in some theorems. Overall, self-consistent achronal ANEC offers a robust principle that preserves causal structure in GR while remaining compatible with quantum field effects in curved spacetime, contingent on remaining within the semiclassical domain.
Abstract
The averaged null energy condition (ANEC) requires that the integral over a complete null geodesic of the stress-energy tensor projected onto the geodesic tangent vector is never negative. This condition is sufficient to prove many important theorems in general relativity, but it is violated by quantum fields in curved spacetime. However there is a weaker condition, which is free of known violations, requiring only that there is no self-consistent space-time in semiclassical gravity in which ANEC is violated on a complete, {\em achronal} null geodesic. We indicate why such a condition might be expected to hold and show that it is sufficient to rule out wormholes and closed timelike curves.