Conformal scattering on the Schwarzschild metric

Nicolas, Jean-Philippe

Annales de l'Institut Fourier, Tome 66 (2016) no. 3, pp. 1175-1216.

Nous montrons que les résultats de décroissance connus en métrique de Schwarzschild sont suffisants pour obtenir une théorie conforme du scattering, que nous ré-interprêtons ensuite comme une théorie analytique définie en termes d’opérateurs d’ondes, avec une dynamique de comparaison explicite associée aux congruences de géodésiques isotropes principales. Le cas de la métrique de Kerr est également discuté.

We show that existing decay results for scalar fields on the Schwarzschild metric are sufficient to obtain a conformal scattering theory. Then we re-interpret this as an analytic scattering theory defined in terms of wave operators, with an explicit comparison dynamics associated with the principal null geodesic congruences. The case of the Kerr metric is also discussed.

Classification : 35L05, 35P25, 35Q75, 83C57
Keywords: Conformal scattering, black holes, wave equation, Schwarzschild metric, Goursat problem
Mot clés : Scattering conforme, trous noirs, équation des ondes, métrique de Schwarzschild, problème de Goursat

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