We have studied nonstationary and nonaxisymmetric perturbations of a magnetohydrodynamic accretion onto a rotating (Kerr) black hole. Assuming that the magnetic field dominates the plasma accretion, we find that the accretion suffers a large radial acceleration resulting from the Lorentz force and becomes highly variable compared with the electromagnetic field on the rotating black hole. In fact, we further find an interesting perturbed structure of the plasma velocity with a large peak in some narrow region located slightly inside of the fast-magnetosonic surface. This is due to the concentrated propagation of the fluid disturbances in the form of fast-magnetosonic waves along the separatrix surface. If the fast-magnetosonic speed is smaller in the polar regions than in the equatorial regions, the critical surface has a prolate shape for radial poloidal field lines. In this case, only the waves that propagate toward the equator can escape from the super-fast-magnetosonic region and collimate poleward as they propagate outward in the sub-fast-magnetosonic regions. We further discuss the capabilities of such collimated waves in accelerating particles due to cyclotron resonance in an electron-positron plasma.
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