Conformal scattering on the Schwarzschild metric
Annales de l'Institut Fourier, Volume 66 (2016) no. 3, p. 1175-1216

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.

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.

Received : 2014-08-21
Revised : 2014-07-13
Accepted : 2015-10-08
Published online : 2016-12-14
DOI : https://doi.org/10.5802/aif.3034
Classification:  35L05,  35P25,  35Q75,  83C57
Keywords: Conformal scattering, black holes, wave equation, Schwarzschild metric, Goursat problem
@article{AIF_2016__66_3_1175_0,
     author = {Nicolas, Jean-Philippe},
     title = {Conformal scattering on the Schwarzschild metric},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {66},
     number = {3},
     year = {2016},
     pages = {1175-1216},
     doi = {10.5802/aif.3034},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2016__66_3_1175_0}
}
Nicolas, Jean-Philippe. Conformal scattering on the Schwarzschild metric. Annales de l'Institut Fourier, Volume 66 (2016) no. 3, pp. 1175-1216. doi : 10.5802/aif.3034. http://www.numdam.org/item/AIF_2016__66_3_1175_0/

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