Kinetic Theory of Collisionless Self-Gravitating Gases: II. Relativistic
  Corrections in Galactic Dynamics
  In this paper we study the kinetic theory of many-particle astrophysical
systems imposing axial symmetry and extending our previous analysis in Phys.
Rev. D 83, 123007 (2011). Starting from a Newtonian model describing a
collisionless self-gravitating gas, we develop a framework to include
systematically the first general relativistic corrections to the matter
distribution and gravitational potentials for general stationary systems. Then,
we use our method to obtain particular solutions for the case of the Morgan &
Morgan disks. The models obtained are fully analytical and correspond to the
post-Newtonian generalizations of classical ones. We explore some properties of
the models in order to estimate the importance of post-Newtonian corrections
and we find that, contrary to the expectations, the main modifications appear
far from the galaxy cores. As a by-product of this investigation we derive the
corrected version of the tensor virial theorem. For stationary systems we
recover the same result as in the Newtonian theory. However, for time dependent
backgrounds we find that there is an extra piece that contributes to the
variation of the inertia tensor.
