The renormalized expectation value of the stress-tensor operator in the Boulware vacuum state is calculated for a massless, conformally coupled scalar field in Schwarzschild space-time. It is found that the difference between the expectation values of the stress tensor in the Boulware and Hartle-Hawking vacua is not isotropic, in contrast with the conjecture of Christensen and Fulling. The results are seen to vindicate the approximation scheme of Brown and Ottewill.

• Received 11 December 1991

DOI:https://doi.org/10.1103/PhysRevD.45.3002