Scattering for the wave equation on the Schwarzschild metric

Details Scattering for the wave equation on the Schwarzschild metric Scattering for the wave equation on the Schwarzschild metric

Apr 1985

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1985gregr..17..353d&link_type=abstract

General Relativity and Gravitation (ISSN 0001-7701), vol. 17, April 1985, p. 353-369.

Astronomy and Astrophysics

Astronomy

14

Black Holes (Astronomy), Field Theory (Physics), Schwarzschild Metric, Wave Equations, Wave Scattering, Asymptotic Properties, Existence Theorems, Minkowski Space, Operators (Mathematics), Scattering Functions

Scientific paper

The scattering problem of a classical massless scalar field propagating on a black-hole background is investigated analytically, constructing wave operators for the horizon and the Minkowski region as distinct asymptotic regions adn proving their existence with the procedure used by Dimock and Kay (1982). The dynamics are formulated in a two-Hilbert-space setting; time-decay estimates are given for free dynamics; the existence of wave operators and inverse wave operators is demonstrated; a proof of asymptotic completeness is presented; and results for an invariant symplectic form which is useful for quantization are discussed.

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