Massive scalar field in multiply connected flat spacetimes.

The vacuum expectation value of the stress-energy tensor 〈0 |Tμν | 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 R3×S1, R2×T 2, R1×T 3, the Möbius strip, and the Klein bottle. In Grant space, which contains nonchronal regions, whether 〈0 |Tμν | 0〉 diverges on a chronology horizon or not depends on the field mass. For a sufficiently large mass 〈0 |Tμν | 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. Typeset using REVTEX