Quantum Inequalities on the Energy Density in Static Robertson-Walker Spacetimes

Abstract

Quantum inequality restrictions on the stress-energy tensor for negative energy are developed for three and four-dimensional static spacetimes. We derive a general inequality in terms of a sum of mode functions which constrains the magnitude and duration of negative energy seen by an observer at rest in a static spacetime. This inequality is evaluated explicitly for a minimally coupled scalar field in three and four-dimensional static Robertson-Walker universes. In the limit of vanishing curvature, the flat spacetime inequalities are recovered. More generally, these inequalities contain the effects of spacetime curvature. In the limit of short sampling times, they take the flat space form plus subdominant curvature-dependent corrections.

18 pages, plain LATEX, with 3 figures, uses epsf

References in corpus (4)

• Averaged Energy Conditions and Quantum Inequalities
• Quantum Field Theory Constrains Traversable Wormhole Geometries
• Restrictions on Negative Energy Density in Flat Spacetime
• The averaged null energy condition and difference inequalities in quantum field theory

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