[Scattering Conforme des champs de Maxwell en l’espace-temps de trou noir de De Sitter–Reissner–Nordström]
Nous construisons une théorie complète de scattering conforme pour les champs de Maxwell dans l’extérieur statique de l’espace-temps de trou noir de De Sitter–Reissner–Nordström. Nous utilisons des résultats de décroissance que nous avons obtenus dans un article séparé, afin de montrer que les opérateurs de trace sont injectifs et d’images fermées. Ensuite, nous résolvons le problème de Goursat pour les champs de Maxwell sur la frontière isotrope ce qui montre que les opérateurs de trace sont surjectifs aussi.
We construct a complete conformal scattering theory for Maxwell fields in the static exterior region of a Reissner–Nordström–de Sitter black hole spacetime. We use uniform energy decay results, which we obtain in a separate paper, to show that the trace operators are injective and have closed ranges. We then solve the Goursat problem (characteristic Cauchy problem) for Maxwell fields on the null boundaries showing that the trace operators are also surjective.
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Accepté le :
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Classification : 35Q61, 35P25, 35Q75, 83C57, 83C50
Mots clés : Scattering conforme, trous noirs, équations de Maxwell, métrique de De Sitter–Reissner–Nordström, problème de Goursat
@article{AIF_2019__69_5_2291_0,
author = {Mokdad, Mokdad},
title = {Conformal {Scattering} of {Maxwell} fields on {Reissner{\textendash}Nordstr\"om{\textendash}de} {Sitter} {Black} {Hole} {Spacetimes}},
journal = {Annales de l'Institut Fourier},
pages = {2291--2329},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {69},
number = {5},
year = {2019},
doi = {10.5802/aif.3295},
language = {en},
url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3295/}
}
Mokdad, Mokdad. Conformal Scattering of Maxwell fields on Reissner–Nordström–de Sitter Black Hole Spacetimes. Annales de l'Institut Fourier, Tome 69 (2019) no. 5, pp. 2291-2329. doi : 10.5802/aif.3295. https://aif.centre-mersenne.org/articles/10.5802/aif.3295/
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