Bounds on negative energy densities in static space-times

TL;DR

This paper derives new, more general quantum inequalities for negative energy densities in static space-times, applicable to various cosmological and black hole backgrounds, strengthening previous bounds without specific sampling function assumptions.

Contribution

It introduces a novel derivation of quantum inequalities for scalar fields in static space-times that do not depend on specific sampling functions, improving previous bounds.

Findings

New quantum inequalities are stronger than previous ones for specific sampling functions.

Bounds are explicitly calculated for Robertson-Walker, de Sitter, and Schwarzschild space-times.

Results constrain negative energy densities in various static backgrounds.

Abstract

Certain exotic phenomena in general relativity, such as backward time travel, appear to require the presence of matter with negative energy. While quantum fields are a possible source of negative energy densities, there are lower bounds - known as quantum inequalities - that constrain their duration and magnitude. In this paper, we derive new quantum inequalities for scalar fields in static space-times, as measured by static observers with a choice of sampling function. Unlike those previously derived by Pfenning and Ford, our results do not assume any specific sampling function. We then calculate these bounds in static three- and four-dimensional Robertson-Walker universes, the de Sitter universe, and the Schwarzschild black hole. In each case, the new inequality is stronger than that of Pfenning and Ford for their particular choice of sampling function.