  We show that the set of ambiguities in the renormalized expected
stress-energy tensor allowed by the Wald axioms is much larger for a massive
scalar field (an infinite number of free parameters) than for a massless scalar
field (two free parameters). We also use the closed-time-path effective action
formalism of Schwinger to calculate the expected value of the stress-energy
tensor in the incoming vacuum state, for a massive scalar field, on any
spacetime which is a linear perturbation off Minkowski spacetime. This result
generalizes an earlier result of Horowitz and also Jordan in the massless case,
and can be used as a testbed for comparing different calculational methods.
