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 in the magnetic null and an efficient process of particle acceleration can occur in its immediate vicinity. Furthermore, the effect of imposed (weak) magnetic field can trigger an onset of chaos in the motion of electrically charged particles. 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 with respect to the central black hole. In this contribution we summarise recent results and we give an outlook for future work with the focus on the role of gravito-magnetic effects caused by rotation of the black hole.
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