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.
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Jensen et al. (1992) studied this question.
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