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.

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Equilibrium configurations of electrically charged perfect fluid surrounding a central rotating black hole endowed with a test electric charge and embedded in a large-scale asymptotically uniform magnetic field are presented. Following our previous studies considering the central black hole non-rotating, we show that in the rotating case, conditions for the configurations existence change according to the spin of the black hole. We focus our attention on the charged fluid in rigid rotation which can form toroidal configurations centered in the equatorial plane or the ones hovering above the black hole, along the symmetry axis. We conclude that a non-zero value of spin changes the existence conditions and the morphology of the solutions significantly. In the case of fast rotation, the morphology of the structures is close to an oblate shape.

The aim of this work is to study the relativistic accretion thick disc model raised by a deformed compact object that slightly deviated from spherical up to the quadrupole moment by utilising the q-metric. This metric is the simplest asymptotically flat solution of Einstein’s equation with quadrupole moment. We studied the effects of quadrupole moments in combination with the parameters of the thick magnetised disc model via studying the properties of these equilibrium sequences of magnetised, non-self-gravitating discs in this space-time. We employed different angular momentum distributions and discussed the procedure of building this toroidal disc model based on a combination of approaches previously considered in the literature. We show the properties of this relativistic accretion disc model and its dependence on the initial parameters. In addition, this theoretical model can serve as the initial data for numerical simulations.