New boundary conditions on the time-like conformal infinity of the Anti-de Sitter universe

Abstract

We investigate the possible propagations of the gravitational waves in 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. The key point is the introduction of a new Hilbert functional framework that contains the massless graviton which is not normalizable in L2. The proof needs the study of the Klein–Gordon equation on R1+6 with a super-singular perturbation of δ0-type.