Quantum inequality in spacetimes with small curvature

TL;DR

This paper derives quantum inequalities for a scalar field in curved spacetimes with small curvature, crucial for ruling out exotic phenomena like closed timelike curves.

Contribution

It provides the first-order correction to flat-space quantum inequalities in spacetimes with small curvature, focusing on the Ricci tensor's role.

Findings

Quantum inequalities are extended to curved spacetimes with small curvature.

No first-order corrections for paths in matter-free regions.

Results help disprove the existence of exotic phenomena like closed timelike curves.

Abstract

Quantum inequalities bound the extent to which weighted time averages of the renormalized energy density of a quantum field can be negative. They have mostly been proved in flat spacetime, but we need curved-spacetime inequalities to disprove the existence of exotic phenomena, such as closed timelike curves. In this work we derive such an inequality for a minimally-coupled scalar field on a geodesic in a spacetime with small curvature, working to first order in the Ricci tensor and its derivatives. Since only the Ricci tensor enters, there are no first-order corrections to the flat-space quantum inequalities on paths which do not encounter any matter or energy.