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Gravitational scattering of electromagnetic field by Schwarzschild black- hole. (English) Zbl 0743.53037

The paper is devoted to the electromagnetic scattering by a spherical black-hole in the Schwarzschild spacetime. Some wave operators are introduced, yielding an electromagnetic field far from the black-hole (\(W_ 0^ \pm\)) and near the Schwarschild radius (\(W^ \pm_ 1\)). The existence of the scattering operator is proved by the Birman-Kato method. The asymptotic completeness of \(W^ +_ 1\) implies that near the horizon, the fields of finite redshifted energy are described by ingoing plane waves. In the Kruskal universe, the same argument for \(W^ \pm_ 0\) and \(W^ +_ 1\) allows the definition of the solution on the future horizons. The scattering operator can be approximated by putting the impedance condition on the stretched horizon, a fact that justifies the Membrane Paradigma D. A. MacDonald and W. M. Suen, Phys. Rev. D 32, 848-871 (1985)].

MSC:

53Z05 Applications of differential geometry to physics
83C22 Einstein-Maxwell equations
53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
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