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Equilibrium configurations of electrically charged perfect fluid surroundinga central rotating black hole endowed with a test electric charge and embeddedin a large-scale asymptotically uniform magnetic field are presented. Followingour previous studies considering the central black hole non-rotating, we showthat in the rotating case, conditions for the configurations existence changeaccording to the spin of the black hole. We focus our attention on the chargedfluid in rigid rotation which can form toroidal configurations centered in theequatorial plane or the ones hovering above the black hole, along the symmetryaxis. We conclude that a non-zero value of spin changes the existenceconditions and the morphology of the solutions significantly. In the case offast rotation, the morphology of the structures is close to an oblate shape.

Equilibrium configurations of charged fluid around Kerr black hole