  In this paper we use the second order formalism of Hartle to study slowly and
rigidly rotating stars with focus on the quadrupole moment of the object. The
second order field equations for the interior fluid are solved numerically for
different classes of possible equations of state and these solutions are then
matched to a vacuum solution that includes the general asymptotically flat
axisymmetric metric to second order, using the Darmois-Israel procedure. For
these solutions we find that the quadrupole moment differs from that of the
Kerr metric, as has also been found for some equations of state in other
studies. Further we consider the post-Minkowskian limit analytically. In the
paper we also illustrate how the relativistic multipole moments can be
calculated from a complex gravitational potential.
