  The Hamiltonian formulation of general relativity (GR) is considered in
finite space-time and a specific frame of reference given by the
diffeo-invariant components of the Fock simplex in terms of the Dirac -- ADM
variables. The evolution parameter and energy invariant with respect to the
time-coordinate transformations are constructed by the separation of the
cosmological scale factor and its identification with the spatial averaging of
the metric determinant, so that the dimension of the kinemetric group of
diffeomorphisms coincides with the dimension of a set of variables whose
velocities are removed by the Gauss-type constraints in accordance with the
second N\"other theorem. This coincidence allows us to solve the energy
constraint, fulfil Dirac's Hamiltonian reduction, and to describe the potential
perturbations in terms of the Lichnerowicz scale-invariant variables
distinguished by the absence of the time derivatives of the spatial metric
determinant. It was shown that the Hamiltonian version of the cosmological
perturbation theory acquires attributes of the theory of superfluid liquid, and
it leads to the generalization of the Schwarzschild solution. The astrophysical
application of this approach to GR is considered under supposition that the
Dirac -- ADM Hamiltonian frame is identified with that of the Cosmic Microwave
Background radiation distinguished by its dipole component in the frame of an
Earth observer.
