  Magnetic null points can develop near the ergosphere boundary of a rotating
black hole by the combined effects of strong gravitational field and the
frame-dragging mechanism. The induced electric component does not vanish an
efficient process of particle acceleration can occur. Furthermore, the effect
of imposed (weak) magnetic field can trigger an onset of chaos. The model
set-up appears to be relevant for low-accretion-rate nuclei of some galaxies
which exhibit episodic accretion events (such as the Milky Way's supermassive
black hole) embedded in a large-scale magnetic field of external origin. We
review our recent results and we give additional context for future work with
the focus on the role of gravito-magnetic effects caused by rotation of the
black hole. While the test motion is strictly regular in the classical black
hole space-time, with and without effects of rotation or electric charge,
gravitational perturbations and imposed external electromagnetic fields may
lead to chaos.
