Vacuum stress tensor in an Einstein universe: Finite-temperature effects

The vacuum average of the stress-energy tensor for a massive scalar field in an Einstein universe is calculated. The renormalization adopted depends on the special circumstance that the WKB approximation is exact on the three-dimensional sphere. The finite results are purely nonperturbative and a renormalization of only the cosmological constant is called for. The finite-temperature corrections have also been considered with the aid of a theory of relativistic time-temperature Green's functions in static space-times. It is shown explicitly that the massless scalar gas is an ideal one satisfying $PV=\frac{E}{3}$.