Complétude asymptotique pour l'équation des ondes dans une classe d'espaces-temps stationnaires et asymptotiquement plats  [ Asymptotic completeness for the wave equation in a class of stationary and asymptotically flat space-times ]
Annales de l'Institut Fourier, Volume 51 (2001) no. 3, p. 779-833

Using a time-dependent method we show asymptotic completeness for the wave equation in a class of stationary and asymptotically flat space-times. We introduce the asymptotic velocity observable and we describe its spectrum (under hypotheses weaker than for asymptotic completeness). The methods used are inspired by those of the analysis of the two-body problem in quantum mechanics.

En utilisant une méthode dépendante du temps, nous démontrons la complétude asymptotique pour l'équation des ondes dans une classe d'espaces-temps stationnaires et asymptotiquement plats. On introduit l'observable de vitesse asymptotique et on décrit son spectre (sous des hypothèses plus faibles que pour la complétude asymptotique). Les méthodes utilisées sont inspirées par celles de l'analyse du problème à deux corps en mécanique quantique.

DOI : https://doi.org/10.5802/aif.1837
Classification:  35L05,  35P25,  35Q75,  58J45,  58J50
Keywords: scattering theory, stationary space-times, wave equation, asymptotic completeness, asymptotic velocity
@article{AIF_2001__51_3_779_0,
     author = {H\"afner, Dietrich},
     title = {Compl\'etude asymptotique pour l'\'equation des ondes dans une classe d'espaces-temps stationnaires et asymptotiquement plats},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {51},
     number = {3},
     year = {2001},
     pages = {779-833},
     doi = {10.5802/aif.1837},
     zbl = {0981.35031},
     mrnumber = {1838466},
     language = {fr},
     url = {http://www.numdam.org/item/AIF_2001__51_3_779_0}
}
Häfner, Dietrich. Complétude asymptotique pour l'équation des ondes dans une classe d'espaces-temps stationnaires et asymptotiquement plats. Annales de l'Institut Fourier, Volume 51 (2001) no. 3, pp. 779-833. doi : 10.5802/aif.1837. http://www.numdam.org/item/AIF_2001__51_3_779_0/

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