Comptes Rendus
Partial Differential Equations/Mathematical Physics
New boundary conditions on the time-like conformal infinity of the Anti-de Sitter universe
Comptes Rendus. Mathématique, Volume 350 (2012) no. 7-8, pp. 359-364.

We investigate the possible propagations of the gravitational waves in the 5-dimensional Anti-de Sitter universe. We construct a large family of unitary dynamics with respect to some high order energies that are conserved and positive. These dynamics are associated with asymptotic conditions on the conformal time-like boundary of the universe. The key point is the introduction of a new Hilbert functional framework that contains the massless graviton which is not normalizable in L2. The proof needs the study of the Klein–Gordon equation on R1+6 with a super-singular perturbation of δ0-type.

Nous étudions diverses propagations possibles des ondes gravitationnelles dans lʼunivers Anti-de Sitter pentadimensionnel. Nous construisons une grande famille de dynamiques unitaires par rapport à des énergies conservées dʼordre élevé et positives. Ces dynamiques sont associées à des conditions asymptotiques au bord conforme de genre temps de lʼunivers. Le point clef est lʼintroduction dʼun nouveau cadre fonctionnel hilbertien qui contient le graviton sans masse, lequel nʼest pas normalisable dans L2. La preuve sʼappuie sur lʼétude de lʼéquation de Klein–Gordon dans R1+6 avec une perturbation super-singulière de type Dirac à lʼorigine.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2012.04.001

Alain Bachelot 1

1 Université de Bordeaux, institut de mathématiques, UMR CNRS 5251, 33405 Talence cedex, France
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Alain Bachelot. New boundary conditions on the time-like conformal infinity of the Anti-de Sitter universe. Comptes Rendus. Mathématique, Volume 350 (2012) no. 7-8, pp. 359-364. doi : 10.1016/j.crma.2012.04.001. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2012.04.001/

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