The Klein-Gordon equation in the Anti-de Sitter Cosmology
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | BACHELOT, Alain | |
| dc.date.accessioned | 2024-04-04T02:18:58Z | |
| dc.date.available | 2024-04-04T02:18:58Z | |
| dc.date.issued | 2011 | |
| dc.identifier.issn | 0021-7824 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/189363 | |
| dc.description.abstractEn | This paper deals with the Klein-Gordon equation on the Poincare chart of the 5-dimensional Anti-de Sitter universe. When the mass mu is larger than -1/4, the Cauchy problem is well-posed despite the loss of global hyperbolicity due to the time-like horizon. 3 We express the finite energy solutions in the form of a continuous Kaluza-Klein tower and we deduce a uniform decay as vertical bar t vertical bar(-3/2) We investigate the case mu = v(2)-1/2, v is an element of N*, which encompasses the gravitational fluctuations, v = 4, and the electromagnetic waves, v = 2. The propagation of the wave front set shows that the horizon acts like a perfect mirror. We establish that the smooth solutions decay as vertical bar t vertical bar(-2-root mu+1/4), and we get global L-P estimates of Strichartz type. When v is even, there appears a lacuna and the equipartition of the energy occurs at finite time for the compactly supported initial data, although the Huygens principle fails. We address the cosmological model of the negative-tension Minkowski brane, on which a Robin boundary condition is imposed. We prove the hyperbolic mixed problem is well-posed and the normalizable solutions can be expanded into a discrete Kaluza-Klein tower. We establish some L-2 - L-infinity estimates in suitable weighted Sobolev spaces. | |
| dc.language.iso | en | |
| dc.publisher | Elsevier | |
| dc.title.en | The Klein-Gordon equation in the Anti-de Sitter Cosmology | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1016/j.matpur.2011.07.004 | |
| dc.subject.hal | Mathématiques [math]/Physique mathématique [math-ph] | |
| bordeaux.journal | Journal de Mathématiques Pures et Appliquées | |
| bordeaux.page | 527-554 | |
| bordeaux.volume | 96 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00959772 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00959772v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Journal%20de%20Math%C3%A9matiques%20Pures%20et%20Appliqu%C3%A9es&rft.date=2011&rft.volume=96&rft.spage=527-554&rft.epage=527-554&rft.eissn=0021-7824&rft.issn=0021-7824&rft.au=BACHELOT,%20Alain&rft.genre=article |
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