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The problem of time is an unsolved issue of canonical General Relativity. A possible solution is the Brown-Kuchar mechanism which couples matter to the gravitational field and recovers a physical, i.e. non vanishing, observable Hamiltonian functional by manipulating the set of constraints. Two cases are analyzed. A generalized scalar fluid model provides an evolutionary picture, but only in a singular case. The Schutz model provides an interesting singularity free result: the entropy per baryon enters the definition of the physical Hamiltonian. Moreover in the co-moving frame one is able to identify the time variable tau with the logarithm of entropy.
The canonical ``loop formulation of quantum gravity is a mathematically well defined, background independent, non perturbative standard quantization of Einsteins theory of General Relativity. Some among the most meaningful results of the theory are:
We study the canonical structure of the topological 3D gravity with torsion, assuming the anti-de Sitter asymptotic conditions. It is shown that the Poisson bracket algebra of the canonical generators has the form of two independent Virasoro algebras
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
In a thorough paper Kuchar has examined the canonical reduction of the most general action functional describing the geometrodynamics of the maximally extended Schwarzschild geometry. This reduction yields the true degrees of freedom for (vacuum) sph
A detailed Gitman-Lyakhovich-Tyutin analysis for higher-order topologically massive gravity is performed. The full structure of the constraints, the counting of physical degrees of freedom, and the Dirac algebra among the constraints are reported. Mo