Oblique magnetic fields and the role of frame dragging near rotating black hole

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.