[Conditions au bord conforme de genre temps de lʼunivers Anti-de Sitter]
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 . La preuve sʼappuie sur lʼétude de lʼéquation de Klein–Gordon dans avec une perturbation super-singulière de type Dirac à lʼorigine.
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 . The proof needs the study of the Klein–Gordon equation on with a super-singular perturbation of -type.
Accepté le :
Publié le :
@article{CRMATH_2012__350_7-8_359_0,
author = {Bachelot, Alain},
title = {New boundary conditions on the time-like conformal infinity of the {Anti-de} {Sitter} universe},
journal = {Comptes Rendus. Math\'ematique},
pages = {359--364},
publisher = {Elsevier},
volume = {350},
number = {7-8},
year = {2012},
doi = {10.1016/j.crma.2012.04.001},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2012.04.001/}
}
TY - JOUR AU - Bachelot, Alain TI - New boundary conditions on the time-like conformal infinity of the Anti-de Sitter universe JO - Comptes Rendus. Mathématique PY - 2012 SP - 359 EP - 364 VL - 350 IS - 7-8 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2012.04.001/ DO - 10.1016/j.crma.2012.04.001 LA - en ID - CRMATH_2012__350_7-8_359_0 ER -
%0 Journal Article %A Bachelot, Alain %T New boundary conditions on the time-like conformal infinity of the Anti-de Sitter universe %J Comptes Rendus. Mathématique %D 2012 %P 359-364 %V 350 %N 7-8 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2012.04.001/ %R 10.1016/j.crma.2012.04.001 %G en %F CRMATH_2012__350_7-8_359_0
Bachelot, Alain. New boundary conditions on the time-like conformal infinity of the Anti-de Sitter universe. Comptes Rendus. Mathématique, Tome 350 (2012) no. 7-8, pp. 359-364. doi : 10.1016/j.crma.2012.04.001. http://www.numdam.org/articles/10.1016/j.crma.2012.04.001/
[1] The Dirac system on the Anti-de Sitter universe, Comm. Math. Phys., Volume 283 (2008), pp. 127-167
[2] The Klein–Gordon equation in Anti-de Sitter cosmology, J. Math. Pures Appl. (9), Volume 96 (2011) no. 6, pp. 527-554
[3] New dynamics in the Anti-de Sitter universe | arXiv
[4] Dynamics in non-globally-hyperbolic, static space-times: III. Anti-de Sitter space–time, Class. Quantum Grav., Volume 21 (2004), pp. 2981-3013
[5] Triplet extensions I: Semibounded operators in the scale of Hilbert spaces, J. Anal. Math., Volume 107 (2009), pp. 251-286
[6] A. Vasy, The wave equation on asymptotically Anti-de Sitter spaces, Analysis and PDE, in press, . | arXiv
Cité par Sources :
