Averaged Energy Inequalities for Non-Minimally Coupled Classical Scalar Fields

TL;DR

This paper establishes local averaged energy inequalities for non-minimally coupled classical scalar fields, demonstrating that certain averaged energy conditions hold even when pointwise conditions fail, with implications for quantum field theory.

Contribution

It introduces averaged energy inequalities for non-minimally coupled scalar fields and shows they satisfy ANEC and AWEC in vacuum spacetimes, laying groundwork for quantum analogues.

Findings

Averages of the stress-energy tensor satisfy specific inequalities.

ANEC and AWEC are valid in vacuum backgrounds.

Results support a classical analogue to the quantum interest conjecture.

Abstract

The stress-energy tensor for the non-minimally coupled scalar field is known not to satisfy the pointwise energy conditions, even on the classical level. We show, however, that local averages of the classical stress-energy tensor satisfy certain inequalities and give bounds for averages along causal geodesics. It is shown that in vacuum background spacetimes, ANEC and AWEC are satisfied. Furthermore we use our result to show that in the classical situation we have an analogue to the so called quantum interest conjecture. These results lay the foundations for averaged energy inequalities for the quantised non-minimally coupled fields.