Averaged Energy Inequalities for the Non-Minimally Coupled Classical Scalar Field

TL;DR

This paper demonstrates that while the classical non-minimally coupled scalar field's stress energy tensor violates point-wise energy conditions, its local averages satisfy certain inequalities, supporting energy bounds like ANEC and AWEC.

Contribution

The paper establishes averaged energy inequalities for the classical non-minimally coupled scalar field, providing foundational results for future quantum field energy bounds.

Findings

Averages along causal geodesics satisfy energy inequalities

ANEC and AWEC hold in Ricci-flat spacetimes

Classical analogue of quantum interest is demonstrated

Abstract

The stress energy tensor for the classical non-minimally coupled scalar field is known not to satisfy the point-wise energy conditions of general relativity. In this paper we show, however, that local averages of the classical stress energy tensor satisfy certain inequalities. We give bounds for averages along causal geodesics and show, e.g., that in Ricci-flat 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 phenomenon of quantum interest. These results lay the foundations for analogous energy inequalities for the quantised non-minimally coupled fields, which will be discussed elsewhere.