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A model for the static weak-field macroscopic medium is analyzed and theequation for the macroscopic gravitational potential is derived. This is abiharmonic equation which is a non-trivial generalization of the Poissonequation of Newtonian gravity. In case of the strong gravitational quadrupolepolarization it essentially holds inside a macroscopic matter source. Outsidethe source the gravitational potential fades away exponentially. The equationis equivalent to a system of the Poisson equation and the nonhomogeneousmodified Helmholtz equations. The general solution to this system is obtainedby using Green's function method and it does not have a limit to Newtoniangravity. In case of the insignificant gravitational quadrupole polarization theequation for macroscopic gravitational potential becomes the Poisson equationwith the matter density renormalized by the factor including the value of thequadrupole gravitational polarization of the source. The general solution tothis equation obtained by using Green's function method has a limit toNewtonian gravity.Comment: 22 pages, no figures, to appear on Class. Quantum Gra

The gravitational polarization in general relativity: solution to Szekeres model of quadrupole polarization