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Classical and quantum scattering theory for linear scalar fields on the Schwarzschild metric. I. (English) Zbl 0628.53080

A general mathematical framework for the scattering of classical linear scalar fields in background gravitational fields, previously developed by the authors, is applied to the covariant Klein-Gordon equation in the exterior Schwarzschild metric. By the help of a suitable set of wave operators they study the asymptotic behaviour of the classical solutions near the Schwarzschild radius and at large distances. Using these classical results the authors discuss the corresponding quantum problem, especially questions concerning the Hawking effect. The Hartle-Hawking and Unruh states are constructed and their asymptotic and horizon behaviour is investigated.
Reviewer: W.Zündahl

MSC:

53C80 Applications of global differential geometry to the sciences
81T20 Quantum field theory on curved space or space-time backgrounds
83C47 Methods of quantum field theory in general relativity and gravitational theory
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