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Stationary and axisymmetric ideal magnetohydrodynamic (MHD) accretion onto ablack hole is studied analytically. The accreting plasma ejected from a plasmasource with low velocity must be super-fast magnetosonic before passing throughthe event horizon. We work out and apply a trans-fast magnetosonic solutionwithout the detailed analysis of the regularity conditions at the magnetosonicpoint, by introducing the bending angle $\beta$ of magnetic field line, whichis the ratio of the toroidal and poloidal components of the magnetic field. Toaccrete onto a black hole, the trans-magnetosonic solution has somerestrictions on $\beta$, which are related to the field-aligned parameters ofthe MHD flows. One of the restrictions gives the boundary condition at theevent horizon for the inclination of a magnetic field line. We find that thisinclination is related to the energy and angular momentum transport to theblack hole. Then, we discuss the spin-up/down process of a rotating black holeby cold MHD inflows in a secular evolution timescale. There are two asymptoticstates for the spin evolution. One is that the angular velocity of the blackhole approaches to that of the magnetic field line, and the other is that thespin-up effect by the positive angular momentum influx and the spin-down effectby the energy influx (as the mass-energy influx) are canceled. We also showthat the MHD inflows prevents the evolution to the maximally rotating blackhole.

Constraints on the Evolution of Black Hole Spin due to Magnetohydrodynamic Accretion