Comptes Rendus
Partial Differential Equations/Mathematical Physics
Scattering by a Minkowski brane world
Comptes Rendus. Mathématique, Volume 347 (2009) no. 21-22, pp. 1243-1248.

We study the wave equation for the gravitational waves in the Randall–Sundrum brane cosmology model. The global Cauchy problem is well posed in the functional framework associated with the energy. The solutions are the sum of a free massless wave propagating on the brane (the graviton), and a superposition of massive Klein–Gordon waves (the Kaluza–Klein tower). We compute the kernel of the truncated resolvent in term of Hankel functions. We develop the complete asymptotic analysis of the Kaluza–Klein towers: L1L and L2L estimates, global Lp Strichartz estimates, existence and asymptotic completeness of the wave operators, computation of the scattering matrix, determination of the resonances on the logarithmic Riemann surface.

Nous étudions l'équation des ondes gravitationnelles dans le modèle de cosmologie branaire de Randall–Sundrum. Le problème de Cauchy global est bien posé dans l'espace des champs d'énergie finie. Les solutions se décomposent de façon unique en la somme d'une onde libre sans masse se propageant sur la brane de Minkowski (le graviton) et d'un somme continue de champs massifs de Klein–Gordon (la tour de Kaluza–Klein). Le résolvant tronqué est explicitement exprimé à l'aide de fonctions de Hankel. Nous faisons l'analyse asymptotique complète des tours de Kaluza–Klein : estimations L1L, L2L, estimations globales Lp de type Strichartz, existence et complétude des opérateurs d'ondes, calcul de la matrice de diffusion, détermination des résonances sur la surface de Riemann du logarithme.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2009.09.004

Alain Bachelot 1

1 Université de Bordeaux, CNRS, institut de mathématiques, 33405 Talence cedex, France
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Alain Bachelot. Scattering by a Minkowski brane world. Comptes Rendus. Mathématique, Volume 347 (2009) no. 21-22, pp. 1243-1248. doi : 10.1016/j.crma.2009.09.004. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.09.004/

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