Null energy conditions outside a background potential

Abstract

We study the Casimir energy of a minimally coupled, real, massless scalar field outside a spherically symmetric background potential. We obtain a general expression for the null energy condition in d dimensions and explicit expressions for a perfectly reflecting spherical boundary in 3+1 and 2+1 dimensions. In these cases, the null energy condition is always violated for radial motion and obeyed for azimuthal motion. Nevertheless, the averaged null energy condition is always obeyed.

17 pages, 7 figures Minor errors in equations (15,26,31-33,35,A5,A6) corrected. Conclusions unaffected. After original publication, we learned of similar work by Saharian (hep-th/0012185)

References in corpus (3)

• Calculating Vacuum Energies in Renormalizable Quantum Field Theories: A New Approach to the Casimir Problem
• Null energy conditions in quantum field theory
• Negative Energy Densities in Quantum Field Theory With a Background Potential

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• Casimir Energies and General Relativity Energy Conditions