Quantum inequalities in two dimensional curved spacetimes

TL;DR

This paper extends quantum inequalities for the stress-energy tensor of a massless scalar field from static to arbitrary curves in two-dimensional curved spacetimes, broadening the understanding of energy constraints in quantum field theory.

Contribution

It generalizes existing bounds to non-static spacetimes and arbitrary observer trajectories using conformal transformations and prior flat spacetime bounds.

Findings

Established a lower bound for energy density along arbitrary curves.

Extended previous static spacetime results to dynamic, curved spacetimes.

Utilized conformal transformations and optimal flat spacetime bounds.

Abstract

We generalize a result of Vollick constraining the possible behaviors of the renormalized expected stress-energy tensor of a free massless scalar field in two dimensional spacetimes that are globally conformal to Minkowski spacetime. Vollick derived a lower bound for the energy density measured by a static observer in a static spacetime, averaged with respect to the observers proper time by integrating against a smearing function. Here we extend the result to arbitrary curves in non-static spacetimes. The proof, like Vollick's proof, is based on conformal transformations and the use of our earlier optimal bound in flat Minkowski spacetime. The existence of such a quantum inequality was previously established by Fewster.