Electrically charged matter in rigid rotation around magnetized black   hole
  We study charged-fluid toroidal structures surrounding a non-rotating charged black hole immersed in a large-scale, asymptotically uniform magnetic field. In continuation of our former study on electrically charged matter in approximation of zero conductivity, we demonstrate existence of orbiting structures in permanent rigid rotation in the equatorial plane, and charged clouds hovering near the symmetry axis. We constrain the range of parameters that allow stable configurations and derive the geometrical shape of equi-pressure surfaces. Our simplified analytical study suggests that these regions of stability may be relevant for trapping electrically charged particles and dust grains in some areas of the black hole magnetosphere, being thus important in some astrophysical situations. 
Ji\v{r}\'i Kov\'a\v{r}, Petr Slan\'y, Claudio Cremaschini, Zden\v{e}k   Stuchl\'ik, Vladim\'ir Karas and Audrey Trova
gr-qc astro-ph.HE