The radial Wheeler--De Witt equation on the asymptotically AdS spacetime proposed in [9] has as its semiclassical solution the wave function that asymptotically satisfies the conformal Ward identity, exemplifying the AdS/CFT correspondence. In this p
aper we show that this results holds also in the case of a complete quantum solution of the radial Wheeler--De Witt equation. It turns out that if the wavefunction is expanded in the parameter $rho$ with $rhorightarrow0$ defines the asymptotic boundary of the spacetime, the quantum loop corrections to the semiclassical wave are of subleading order.
The Brown-Kuchar mechanism is applied in the case of General Relativity coupled with the Schutz model for a perfect fluid. Using the canonical formalism and manipulating the set of modified constraints one is able to recover the definition of a time
evolution operator, i.e. a physical Hamiltonian, expressed as a functional of gravitational variables and the entropy.
