  We obtain an approximate global stationary and axisymmetric solution of
Einstein's equations which can be considered as a simple star model: a
self-gravitating perfect fluid ball with constant mass density rotating in
rigid motion. Using the post-Minkowskian formalism (weak-field approximation)
and considering rotation as a perturbation (slow-rotation approximation), we
find approximate interior and exterior (asymptotically flat) solutions to this
problem in harmonic and quo-harmonic coordinates. In both cases, interior and
exterior solutions are matched, in the sense of Lichnerowicz, on the surface of
zero pressure to obtain a global solution. The resulting metric depends on
three arbitrary constants: mass density, rotational velocity and the star
radius at the non-rotation limit. The mass, angular momentum, quadrupole moment
and other constants of the exterior metric are determined by these three
parameters. It is easy to show that this type of fluid cannot be a source of
the Kerr metric
