Stress-energy of a quantized scalar field in static wormhole spacetimes

Static traversable wormhole solutions of the Einstein equations require ``exotic'' matter which violates the weak energy condition. The vacuum stress-energy of quantized fields has been proposed as the source for this matter. Using the Dewitt-Schwinger approximation, analytic expressions for the stress-energy of a quantized massive scalar field are calculated in five static, spherically symmetric Lorentzian wormhole spacetimes. We do not attempt to solve the self-consistent semiclassical Einstein equations but instead work in the test-field limit. We find that in all five cases, for both minimally and conformally coupled scalar fields, the stress-energy does not even qualitatively have the properties needed to support the wormhole geometry.