no. 3
Scattering theory for Dirac fields near an extreme Kerr–de Sitter black hole
[Théorie de la diffusion pour des champs de Dirac au voisinage d’un trou noir extrême de type Kerr–de Sitter]
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)
Annales de l'Institut Fourier, Tome 73 (2023) no. 3, pp. 919-997.

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.

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.

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DOI : 10.5802/aif.3553
Classification : 35P25, 35Q75, 83C57, 35Q41
Keywords: Scattering, extremal black hole, Kerr–de Sitter blackhole, Dirac equation, Mourre theory.
Mot clés : Scattering, trou noir extrême, trou noir de de Sitter–Kerr, équation de Dirac, théorie de Mourre.
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)
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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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, Tome 73 (2023) no. 3, pp. 919-997. doi : 10.5802/aif.3553. https://aif.centre-mersenne.org/articles/10.5802/aif.3553/

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