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