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

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

2011-12-28

arxiv.org/abs/1112.6138v2

Physics

Mathematical Physics

Scientific paper

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.

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