  We numerically investigate the motion of stars on the meridional plane of an
axially symmetric disk galaxy model, containing a central supermassive black
hole, represented by the Paczynski-Wiita potential. By using this
pseudo-Newtonian potential we can replicate important relativistic properties,
such as the existence of the Schwarzschild radius. After classifying extensive
samples of initial conditions of trajectories, we manage to distinguish between
collisional, ordered, and chaotic motion. Besides, all starting conditions of
regular orbits are further classified into families of regular orbits. Our
results are presented through modern color-coded basin diagrams on several
types of two-dimensional planes. Our analysis reveals that both the mass of the
black hole (in direct relation with the Schwarzschild radius) as well as the
angular momentum play an important role in the character of orbits of stars.
More specifically, the trajectories of low angular momentum stars are highly
affected by the mass of the black hole, while high angular momentum stars seem
to be unaffected by the central black hole. Comparison with previous related
outcomes, using Newtonian potentials for the central region of the galaxy, is
also made.
