The energy-momentum tensor near a black hole

The energy-momentum tensor for a conformally invariant scalar field near a Schwarzschild black hole in thermal equilibrium with radiation is found by a combination of analytical and numerical techniques. Calculations are performed in the Euclidean section of the spacetime, and divergences isolated using the heat kernel expansion. It is found that the results agree well with those of Candelas 1], but that there are significant differences from the Gaussian approximation of Page 2].