Bounds on negative energy densities in static space-times

Christopher J. Fewster; Edward Teo

doi:10.1103/PhysRevD.59.104016

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Bounds on negative energy densities in static space-times

Christopher J. Fewster^*

Edward Teo^†

Department of Mathematics, University of York, Heslington, York YO10 5DD, England

Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, England
Department of Physics, National University of Singapore, Singapore 119260

^*Electronic address: cjf3@york.ac.uk
^†Electronic address: E.Teo@damtp.cam.ac.uk

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Phys. Rev. D 59, 104016 – Published 23 April, 1999

DOI: https://doi.org/10.1103/PhysRevD.59.104016

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.

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[c21] P. Candelas, Phys. Rev. D 21, 2185 (1980).

[c22] B.P. Jensen, J.G. McLaughlin, and A.C. Ottewill, Phys. Rev. D 45, 3002 (1992).

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Bounds on negative energy densities in static space-times

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