New Dynamics in the Anti-De Sitter Universe AdS^5

Abstract

This paper deals with the propagation of the gravitational waves in the Poincaré patch of 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. This result does not contradict the statement of Breitenlohner-Freedman that the hamiltonian is essentially self-adjoint in L2 and thus accordingly the dynamics is uniquely determined. The key point is the introduction of a new Hilbert functional framework that contains the massless graviton which is not normalizable in L2. Then the hamiltonian is not essentially self-adjoint in this new space and admits a lot of positive self-adjoint extensions.

References in corpus (4)

• Dynamics in Non-Globally-Hyperbolic Static Spacetimes III: Anti-de Sitter Spacetime
• The Dirac system on the Anti-de Sitter Universe
• On the Interplay of Regularity and Decay in Case of Radial Functions I. Inhomogeneous spaces
• Completeness of non-normalizable modes

Cited by in corpus (3)

• The holographic Hadamard condition on asymptotically Anti-de Sitter spacetimes
• Determining an asymptotically AdS spacetime from data on its conformal boundary
• Quasimodes and a lower bound for the local energy decay of the Dirac equation in Schwarzschild-Anti-de Sitter spacetime