Quantum energy inequalities in two dimensions

TL;DR

This paper extends quantum energy inequalities for massless scalar fields from flat to all two-dimensional globally hyperbolic spacetimes, showing flat spacetime QEIs approximate curved spacetime results on short sampling times, aiding exotic spacetime constraints.

Contribution

It generalizes QEIs to all 2D globally hyperbolic spacetimes and demonstrates their approximation validity on short timescales.

Findings

QEIs hold in all 2D globally hyperbolic spacetimes

Flat spacetime QEIs approximate curved spacetime results on short timescales

Results are relevant for constraining exotic spacetime metrics

Abstract

Quantum energy inequalities (QEIs) were established by Flanagan for the massless scalar field on two-dimensional Lorentzian spacetimes globally conformal to Minkowski space. We extend his result to all two-dimensional globally hyperbolic Lorentzian spacetimes and use it to show that flat spacetime QEIs give a good approximation to the curved spacetime results on sampling timescales short in comparison with natural geometric scales. This is relevant to the application of QEIs to constrain exotic spacetime metrics.