MASSIVE SCALAR FIELD IN MULTIPLY CONNECTED FLAT SPACETIMES

The vacuum expectation value of the stress-energy tenser [0\T-mu nu\0] is calculated in several multiply connected flat spacetimes for a mas sive scalar field with arbitrary curvature coupling. We find that a no nzero field mass always decreases the magnitude of the energy density in chronology-respecting manifolds such as R(3) X S-1, R(2) X T-2, R(1 ) X T-3, the Mobius strip, and the Klein bottle. In Grant space, which contains nonchronal regions, whether or not [0\T-mu nu\0] diverges on a chronology horizon depends on the field mass. For a sufficiently la rge mass [0\T-mu nu\0] remains finite, and the metric back reaction ca used by a massive quantised field may not be large enough to significa ntly change the Grant space geometry.