  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.

High Energy Astrophysical Phenomena