  A pseudo-Newtonian Hill problem based on the Paczynski-Wiita pseudo-Newtonian
potential that reproduces general relativistic effects is presented and
compared with the usual Newtonian Hill problem. Poincare maps, Lyapunov
exponents and fractal escape techniques are employed to study bounded and
unbounded orbits. In particular we consider the systems composed by Sun, Earth
and Moon and composed by the Milky Way, the M2 cluster and a star. We find that
some pseudo-Newtonian systems - including the M2 system - are more stable than
their Newtonian equivalent.
