  The problem of construction of a continuous (macroscopic) matter model for a
given point-like (microscopic) matter distribution in general relativity is
formulated. The existing approaches are briefly reviewed and a physical analogy
with the similar problem in classical macroscopic electrodynamics is pointed
out. The procedure by Szekeres in the linearized general relativity on
Minkowski background to construct a tensor of gravitational quadruple
polarization by applying Kaufman's method of molecular moments for derivation
of the polarization tensor in macroscopic electrodynamics and to derive an
averaged field operator by utilizing an analogy between the linearized Bianchi
identities and Maxwell equations, is analyzed. It is shown that the procedure
has some inconsistencies, in particular, (1) it has only provided the terms
linear in perturbations for the averaged field operator which do not contribute
into the dynamics of the averaged field, and (2) the analogy between
electromagnetism and gravitation does break upon averaging. A macroscopic
gravity approach in the perturbation theory up to the second order on a
particular background space-time taken to be a smooth weak gravitational field
is applied to write down a system of macroscopic field equations: Isaacson's
equations with a source incorporating the quadruple gravitational polarization
tensor, Isaacson's energy-momentum tensor of gravitational waves and
energy-momentum tensor of gravitational molecules and corresponding equations
of motion. A suitable set of material relations which relate all the tensors is
proposed.
