Axially Symmetric Post-Newtonian Stellar Systems

We introduce a method to obtain self-consistent, axially symmetric, thin disklike stellar models in the first post-Newtonian (1PN) approximation. The models obtained are fully analytical and corresponds to the post-Newtonian generalizations of classical ones. By introducing in the field equations provided by the 1PN approximation a known distribution function (DF) corresponding to a Newtonian model, two fundamental equations determining the 1PN corrections are obtained, which are solved using the Hunter method. The rotation curves of the 1PN-corrected models differs from the classical ones and, for the generalized Kalnajs discs, the 1PN corrections are clearly appreciable with values of the mass and radius of a typical galaxy. On the other hand, the relativistic mass correction can be ignored for all models.