Averaged null energy condition violation in a conformally flat spacetime

TL;DR

This paper demonstrates that the averaged null energy condition can be violated by a conformally coupled scalar field in conformally flat spacetimes, with violations depending on quantum states and not solely on anomalies.

Contribution

It shows that the averaged null energy condition can be violated in conformally flat spacetimes by quantum scalar fields, independent of anomalies.

Findings

Violations depend on quantum state and can be arbitrarily large.

Achronal averaged null energy condition is also violated.

Violations are not solely due to anomalies.

Abstract

We show that the averaged null energy condition can be violated by a conformally coupled scalar field in a conformally flat spacetime in 3+1 dimensions. The violation is dependent on the quantum state and can be made as large as desired. It does not arise from the presence of anomalies, although anomalous violations are also possible. Since all geodesics in conformally flat spacetimes are achronal, the achronal averaged null energy condition is likewise violated.