The exact superposition of a central static black hole with surrounding thindisk in presence of a magnetic field is investigated. We consider two models ofdisk, one of infinite extension based on a Kuzmin-Chazy-Curzon metric and otherfinite based on the first Morgan-Morgan disk. We also analyze a simple model ofactive galactic nuclei consisting of black hole, a Kuzmin-Chazy-Curzon disk andtwo rods representing jets, in presence of magnetic field. To explain thestability of the disks we consider the matter of the disk made of twopressureless streams of counterrotating charged particles (counterrotatingmodel) moving along electrogeodesic. Using the Rayleigh criterion we derivatefor circular orbits the stability conditions of the particles of the streams.The influence of the magnetic field on the matter properties of the disk and onits stability are also analyzed.
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