Post – Newtonian Approximation and Maclaurin Spheroids

There is a natural relationship to the post-Newtonian expansion scheme that is used to describe sources of gravity which are not too far from Newtonian, i.e, not too relativistic. Here the expantion can lead to the solutions for the exterior fields of such sources. Till now the post-Newtonian expansion known to high order, in some cases 8 th order. This paper has provided a high order expansion of the vacuum axisymmetric equations and also shows how some of our expanded terms relate to the known post-Newtonian ones for the particular case of homogeneous rotating bodies (generalized Maclaurin spheroids).