Scale anomalies imply violation of the averaged null energy condition

TL;DR

This paper investigates the violation of the averaged null energy condition (ANEC) in quantum field theory on curved spacetimes, identifying broad classes of spacetimes where ANEC does not hold, with implications for understanding energy conditions in quantum gravity.

Contribution

The paper characterizes a broad class of spacetimes where the ANEC is guaranteed to be violated, extending previous results and providing new insights into quantum energy conditions.

Findings

Identifies classes of spacetimes violating ANEC

Analyzes implications for quantum field theory in curved spacetime

Discusses ANEC violation in Schwarzschild spacetime

Abstract

Considerable interest has recently been expressed regarding the issue of whether or not quantum field theory on a fixed but curved background spacetime satisfies the averaged null energy condition (ANEC). A comment by Wald and Yurtsever [Phys. Rev. D43, 403 (1991)] indicates that in general the answer is no. In this note I explore this issue in more detail, and succeed in characterizing a broad class of spacetimes in which the ANEC is guaranteed to be violated. Finally, I add some comments regarding ANEC violation in Schwarzschild spacetime.