Stress-energy tensor of quantized scalar fields in static spherically symmetric spacetimes

A method for computing the stress-energy tensor of quantized scalar fields in static spherically symmetric spacetimes is described. The fields can be massless or massive with an arbitrary coupling {ξ} to the scalar curvature. They can be either in a zero temperature vacuum state or a nonzero temperature thermal state. Analytical approximations which apply to all of these cases are obtained. The method is used to numerically compute the components of the stress-energy tensor of massive and massless scalar fields in Schwarzschild and Reissner-Nordstr\"om spacetimes. The results are compared to the analytical approximations and the accuracy of the analytical approximations is discussed.