  The post-Newtonian Jeans equation for stationary self-gravitating systems is
derived from the post-Newtonian Boltzmann equation in spherical coordinates.
The Jeans equation is coupled with the three Poisson equations from the
post-Newtonian theory. The Poisson equations are functions of the
energy-momentum tensor components which are determined from the post-Newtonian
Maxwell--J\"uttner distribution function. As an application, the effect of a
central massive black hole on the velocity dispersion profile of the host
galaxy is investigated and the influence of the post-Newtonian corrections are
determined.
