  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.
