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Zbl 0743.53037
Bachelot, A.
Gravitational scattering of electromagnetic field by Schwarzschild black- hole. (English)
[J] Ann. Inst. Henri Poincaré, Phys. Théor. 54, No.3, 261-320 (1991). ISSN 0246-0211

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 ($W\sb 0\sp \pm$) and near the Schwarschild radius ($W\sp \pm\sb 1$). The existence of the scattering operator is proved by the Birman-Kato method. The asymptotic completeness of $W\sp +\sb 1$ 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 $W\sp \pm\sb 0$ and $W\sp +\sb 1$ 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 {\it D. A. MacDonald} and {\it W. M. Suen}, Phys. Rev. D 32, 848-871 (1985)].
[G.Pripoae (Bucureşti)]

MSC 2000:: *53Z05 Appl. of differential geometry to physics
83C22 Electromagnetic fields, Einstein-Maxwell equations
53C50 Lorentz manifolds, manifolds with indefinite metrics

Keywords: electromagnetic scattering; black-hole; Schwarzschild spacetime; Kruskal universe; scattering operator; Membrane Paradigm

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