One-loop Quantum Gravity in Schwarzschild Spacetime

Abstract

The quantum theory of linearized perturbations of the gravitational field of a Schwarzschild black hole is presented. The fundamental operators are seen to be the perturbed Weyl scalars ${\dot{\Psi }}_0$ and ${\dot{\Psi }}_4$ associated with the Newman-Penrose description of the classical theory. Formulae are obtained for the expectation values of the modulus squared of these operators in the Boulware, Unruh and Hartle-Hawking quantum states. Differences between the renormalized expectation values of both $|{\dot{\Psi }}_0{|}^2$ and $|{\dot{\Psi }}_4{|}^2$ in the three quantum states are evaluated numerically.

39 pages, 11 Postscript figures, using revtex

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