Pair plasma production in a force-free magnetosphere around a supermassive black hole

We quantitatively solve the problem of plasma supply to the stationary, axisymmetric, force-free magnetosphere of a rotating black hole residing in an active galactic nucleus. At the plasma source from which both inflowing and outflowing charge-separated plasmas originate, the shortage of charge will lead to the emergence of a strong electric field along the magnetic field line. The parallel electric field accelerates migratory electrons and/or positrons to ultrarelativistic energies. These relativistic electrons/positrons scatter background photons to produce high-energy gamma-rays that can materialize as pairs by colliding with background photons. The produced pairs replenish the inflowing and outflowing charges and are accelerated to result in a stationary pair production cascade. It is demonstrated that a sufficient amount of plasma can be supplied for the Blandford-Znajek process to work effectively.