Abstract
The Dirac scheme of the canonical formalism is formulated for the description of an interacting system consisting of matter and the gravitational field; this scheme is applied to a spherical distribution of a perfect fluid in the case of a maximally hard equation of state; an exact special solution of the corresponding canonical equations is obtained; the ADM method is used to construct the true Hamiltonian of the system consisting of a perfect fluid and the gravitational field; ways to quantize the model are considered.
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