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General relativistic magnetohydrodynamic (GRMHD) flows along magnetic fieldsthreading a black hole can be divided into inflow and outflow parts, accordingto the result of the competition between the black hole gravity andmagneto-centrifugal forces along the field line. Here we present the firstself-consistent, semi-analytical solution for a cold, Poynting flux-dominated(PFD) GRMHD flow, which passes all four critical (inner and outer, Alfven andfast magnetosonic) points along a parabolic streamline. By assuming that thedominating (electromagnetic) component of the energy flux per flux tube isconserved at the surface where the inflow and outflow are separated, theoutflow part of the solution can be constrained by the inflow part. Thesemi-analytical method can provide fiducial and complementary solutions forGRMHD simulations around the rotating black hole, given that the black holespin, global streamline, and magnetizaion (i.e., a mass loading at theinflow/outflow separation) are prescribed. For reference, we demonstrate aself-consistent result with the work by McKinney in a quantitative level.

Steady General Relativistic Magnetohydrodynamic Inflow/Outflow Solution along Large-Scale Magnetic Fields that Thread a Rotating Black Hole