  We study some exact and approximate solutions of Einstein's equations that
can be used to describe the gravitational field of astrophysical compact
objects in the limiting case of slow rotation and slight deformation. First, we
show that none of the standard models obtained by using Fock's method can be
used as an interior source for the approximate exterior Kerr solution. We then
use Fock's method to derive a generalized interior solution, and also an
exterior solution that turns out to be equivalent to the exterior Hartle-Thorne
approximate solution that, in turn, is equivalent to an approximate limiting
case of the exact Quevedo-Mashhoon solution. As a result we obtain an analytic
approximate solution that describes the interior and exterior gravitational
field of a slowly rotating and slightly deformed astrophysical object.
