The Klein-Gordon equation in the Anti-de Sitter Cosmology
Idioma
en
Article de revue
Este ítem está publicado en
Journal de Mathématiques Pures et Appliquées. 2011, vol. 96, p. 527-554
Elsevier
Resumen en inglés
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 ...Leer más >
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.< Leer menos
Orígen
Importado de HalCentros de investigación