Massive scalar field in multiply connected flat spacetimes

Abstract

The vacuum expectation value of the stress-energy tensor $⟨0\left|T_{\mu \nu }\right|0⟩$ is calculated in several multiply connected flat spacetimes for a massive scalar field with arbitrary curvature coupling. We find that a nonzero field mass always decreases the magnitude of the energy density in chronology-respecting manifolds such as $R^3\times S^1$, $R^2\times T^2$, $R^1\times T^3$, the Möbius strip, and the Klein bottle. In Grant space, which contains nonchronal regions, whether $⟨0\left|T_{\mu \nu }\right|0⟩$ diverges on a chronology horizon or not depends on the field mass. For a sufficiently large mass $⟨0\left|T_{\mu \nu }\right|0⟩$ remains finite, and the metric backreaction caused by a massive quantized field may not be large enough to significantly change the Grant space geometry.

19 pages, REVTeX, 5 figures in separate uuencoded compressed file

References in corpus (2)

• Cosmic Strings and Chronology Protection
• Quantum Field Theory in Spaces with Closed Time-Like Curves

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