Regular and Chaotic Motion in General Relativity. Case of Magnetized Black Hole and a Massive Magnetic Dipole

Near a rotating black hole, circular motion of particles, dust grains and complex fluids have been investigated as a model for accretion of gaseous and dusty environment in the toroidal geometry. Here we further discuss, within the framework of general relativity, figures of equilibrium of matter under the influence of combined gravitational and large-scale magnetic fields, assuming that the accreted material acquires a small (but non-vanishing) electric charge due to the interplay of plasma processes and photoionization. We employ different solutions for the central body (magnetized Kerr metric, or a massive magnetic dipole) and we identify the corresponding regions of stability.

The action of gravitational and electromagnetic forces jointly determine the regions of stable motion, in particular, whether the halo lobes develop where particles can be captured in permanent circulation around the central body. Therefore, our set-up is relevant in the context of accreting compact objects where the halo motion can describe the overall global motion through corona of an accretion disc or a geometrically thick torus. We also investigate situations when the motion exhibits the onset of chaos. In order to characterize the measure of chaoticness we employ techniques of Poincare surfaces of section and Recurrence plots.

Acknowledgments: Czech-US collaboration project (ref. ME09036) and the Czech Science Foundation program (ref. P209/10/P190) are gratefully acknowledged for their continued support.