Absolute quantum energy inequalities in curved spacetime

TL;DR

This paper derives the first explicit, geometry-dependent quantum energy inequality for the Klein-Gordon field in curved spacetime, providing a local bound on negative energy densities that is covariant and applicable to various states.

Contribution

It introduces the first absolute quantum energy inequality in four-dimensional curved spacetime, depending solely on local geometry and applicable to adiabatic states.

Findings

First explicit absolute QEI for Klein-Gordon field in curved spacetime.

Bound depends only on local geometric properties.

Results are covariant and applicable to a broad class of states.

Abstract

Quantum Energy Inequalities (QEIs) are results which limit the extent to which the smeared renormalised energy density of the quantum field can be negative, when averaged along a timelike curve or over a more general timelike submanifold in spacetime. On globally hyperbolic spacetimes the minimally-coupled massive quantum Klein--Gordon field is known to obey a `difference' QEI that depends on a reference state chosen arbitrarily from the class of Hadamard states. In many spacetimes of interest this bound cannot be evaluated explicitly. In this paper we obtain the first `absolute' QEI for the minimally-coupled massive quantum Klein--Gordon field on four dimensional globally hyperbolic spacetimes; that is, a bound which depends only on the local geometry. The argument is an adaptation of that used to prove the difference QEI and utilises the Sobolev wave-front set to give a complete characterisation of the singularities of the Hadamard series. Moreover, the bound is explicit and can be formulated covariantly under additional (general) conditions. We also generalise our results to incorporate adiabatic states.