%0 Journal Article
%T New Dynamics in the Anti-De Sitter Universe AdS^5
%A Alain Bachelot
%J Mathematics
%D 2011
%I arXiv
%R 10.1007/s00220-013-1690-5
%X This paper deals with the propagation of the gravitational waves in the Poincar\'e 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.
%U http://arxiv.org/abs/1112.6138v2