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.
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.
@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},
volume = {51},
year = {2001},
pages = {779-833},
doi = {10.5802/aif.1837},
mrnumber = {1838466},
zbl = {0981.35031},
language = {fr},
url = {http://dml.mathdoc.fr/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, Tome 51 (2001) pp. 779-833. doi : 10.5802/aif.1837. http://gdmltest.u-ga.fr/item/AIF_2001__51_3_779_0/
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