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Asymptotic completeness for the Klein-Gordon equation on the Schwarzschild metric. (English) Zbl 0809.35141

Summary: We prove the strong asymptotic completeness of the wave operators, classic at the horizon and Dollard-modified at infinity, describing the scattering of a massive Klein-Gordon field by a Schwarzschild black hole. The scattering operator is unitarily implementable in the Fock space of free fields.

MSC:

35Q75 PDEs in connection with relativity and gravitational theory
83C47 Methods of quantum field theory in general relativity and gravitational theory
85A15 Galactic and stellar structure
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