  A solution of the Einstein's equations that represents the superposition of a
Schwarszchild black hole with both quadrupolar and octopolar terms describing a
halo is exhibited. We show that this solution, in the Newtonian limit, is an
analog to the well known H\'enon-Heiles potential. The integrability of orbits
of test particles moving around a black hole representing the galactic center
is studied and bounded zones of chaotic behavior are found.
