  We examine Poynting flux generation due to pair plasma accreting onto a
slowly rotating black hole. In particular, we consider the possibility of an
outgoing flux at the horizon. Our approach is based on a two-fluid model
representing a collisionless pair plasma. In the background, the plasma inflow
is neutral and radial along the magnetic field lines of a split monopole in a
Schwarzschild spacetime. A combined mechanism of dragging by the black hole's
spin and the Lorentz force produces charge separation and current flow, and
hence electric and toroidal magnetic fields. By WKB analysis, two classes of
solutions of perturbation equations for small black hole spin are identified:
one is related to inward flux, and the amplitude inwardly increases; the other
generates an outward flux with a peak position around $r=3M$, tending to zero
at the horizon. The power induced by the two-fluid effect is inversely
proportional to plasma density, and is small in almost all astrophysical
situations. A magnetic vacuum region is located elsewhere for effective
Poynting flux generation.
