Averaged null energy condition violation in a conformally flat spacetime

Understand

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.