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

TL;DR

This paper explores new gravitational wave dynamics in a 5D Anti-de Sitter universe, introducing a novel mathematical framework that allows for multiple stable evolutions beyond traditional self-adjoint Hamiltonian constraints.

Contribution

It constructs a family of unitary dynamics for gravitational waves in AdS^5 using a new Hilbert space framework that includes non-normalizable massless gravitons.

Findings

Multiple positive self-adjoint extensions of the Hamiltonian are possible.

The dynamics are consistent with boundary conditions at the conformal boundary.

The framework accommodates non-normalizable modes like the massless graviton.

Abstract

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.