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This paper studies steady axisymmetric flows of a relativistic ideal magnetohydrodynamical (MHD) fluid in the magnetosphere of a Kerr black hole. It is assumed that an inward flow due to the strong gravity and a centrifugally driven outward flow originate from the plasma's source with zero poloidal velocity. The MHD flows must become super-Alfvenic to fall into the event horizon or reach infinity along the magnetic field lines. The approach is to analyze the poloidal flow equation at the Alfven surface. The solutions are characterized by the angular velocity of the magnetic field lines and the positions of the plasma injection and the Alfven point. It is also found that the MHD inflow can carry a negative energy flux into the event horizon. This result is discussed in relation to the energy extraction from the rotating black hole and the acceleration of winds or jets.
Takahashi et al. (Thu,) studied this question.