New Dynamics in the Antide Sitter Universe AdS ^{5}
Abstract
This paper deals with the propagation of the gravitational waves in the Poincaré patch of the 5dimensional Antide 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 timelike boundary of the universe. This result does not contradict the statement of BreitenlohnerFreedman that the hamiltonian is essentially selfadjoint in L ^{2} 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 L ^{2}. Then the hamiltonian is not essentially selfadjoint in this new space and possesses a lot of different positive selfadjoint extensions. These dynamics satisfy a holographic principle: there exists a renormalized boundary value which completely characterizes the whole field in the bulk.
 Publication:

Communications in Mathematical Physics
 Pub Date:
 June 2013
 DOI:
 10.1007/s0022001316905
 arXiv:
 arXiv:1112.6138
 Bibcode:
 2013CMaPh.320..723B
 Keywords:

 Mathematical Physics;
 35Q75;
 83C35;
 47B25
 EPrint:
 Comm. Math. Phys., 320 (2013), 723759