Quantum Stress Tensor in Schwarzschild Space-Time

The vacuum expectation value of the stress-energy tensor for the Hartle-Hawking state in Schwarzschild space-time has been calculated for the conformal scalar field. $〈T_{\mu }^{\nu }〉$ separates naturally into the sum of two terms. The first coincides with an approximate expression suggested by Page. The second term is a "remainder" that may be evaluated numerically. The total expression is in good qualitative agreement with Page's approximation. These results are at variance with earlier results by Fawcett whose error is explained.