Scattering theory for Dirac fields near an extreme Kerr–de Sitter black hole
Annales de l'Institut Fourier, Online first, 79 p.

In this paper, we construct a scattering theory for classical massive Dirac fields near the “double” horizon of an extreme Kerr–de Sitter blackhole. Our main tool is the existence of a conjugate operator in the sense of Mourre theory. Additionally, despite the fact that effects of the rotation are “amplified” near the double horizon, we show that one can still reduce our study to a 1-dimensional problem through an appropriate decomposition of the Hilbert space.

Dans cet article, nous développons une théorie de la diffusion pour des champs de Dirac massifs en métrique Kerr–de Sitter extrême, dans la région située entre l’horizon (double) du trou noir et l’horizon cosmologique. L’outil principal de la construction est l’existence d’un opérateur conjugué au sens de la théorie de Mourre. Par ailleurs, bien que les effets de la rotation soient amplifiées au voisinage de l’horizon double, nous montrons qu’il est néanmoins possible de se ramener à un problème de diffusion unidimensionnelle moyennant une décomposition ad-hoc de l’espace de Hilbert.

Received:
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Accepted:
Online First:
DOI: 10.5802/aif.3553
Classification: 35P25,  35Q75,  83C57,  35Q41
Keywords: Scattering, extremal black hole, Kerr–de Sitter blackhole, Dirac equation, Mourre theory.
Borthwick, Jack A. 1

1 Univ. Brest UMR CNRS 6205 Laboratoire de Mathématiques de Bretagne Atlantique 6. av Victor Le Gorgeu CS 93837 29238 BREST cedex 3 (France)
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Borthwick, Jack A. Scattering theory for Dirac fields near an extreme Kerr–de Sitter black hole. Annales de l'Institut Fourier, Online first, 79 p.

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