  General relativistic magnetohydrodynamic (GRMHD) flows along magnetic fields
threading a black hole can be divided into inflow and outflow parts, according
to the result of the competition between the black hole gravity and
magneto-centrifugal forces along the field line. Here we present the first
self-consistent, semi-analytical solution for a cold, Poynting flux-dominated
(PFD) GRMHD flow, which passes all four critical (inner and outer, Alfven and
fast magnetosonic) points along a parabolic streamline. By assuming that the
dominating (electromagnetic) component of the energy flux per flux tube is
conserved at the surface where the inflow and outflow are separated, the
outflow part of the solution can be constrained by the inflow part. The
semi-analytical method can provide fiducial and complementary solutions for
GRMHD simulations around the rotating black hole, given that the black hole
spin, global streamline, and magnetizaion (i.e., a mass loading at the
inflow/outflow separation) are prescribed. For reference, we demonstrate a
self-consistent result with the work by McKinney in a quantitative level.
