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SCATTERING OF MASSLESS DIRAC FIELDS BY A KERR BLACK HOLE

M.A.B., UMR CNRS no 5466, Institut de Mathématiques de Bordeaux, Université Bordeaux 1, 351 cours de la Libération, 33405 Talence cedex, France

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JEAN-PHILIPPE NICOLAS

M.A.B., UMR CNRS no 5466, Institut de Mathématiques de Bordeaux, Université Bordeaux 1, 351 cours de la Libération, 33405 Talence cedex, France

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https://doi.org/10.1142/S0129055X04001911Cited by:35 (Source: Crossref)

Abstract

For the massless Dirac equation outside a slow Kerr black hole, we prove asymptotic completeness. We introduce a new Newman–Penrose tetrad in which the expression of the equation contains no artificial long-range perturbations. The main technique used is then a Mourre estimate. The geometry near the horizon requires us to apply a unitary transformation before we find ourselves in a situation where the generator of dilations is a good conjugate operator. The results are eventually re-interpreted geometrically to provide the solution to a Goursat problem on the Penrose compactified exterior.

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