On magnetospheres of spinning black holes

Spinning black holes in magnetic fields are though to develop force-free magnetospheres. Their structure is a key to the energy extraction via Blandford-Znajek mechanism, which can power extended relativistic jets of active galactic nuclei. The key assumption for the force-free condition is the presence electron-positron plasma with the density being above the Goldreigh-Julian density. Here we explore the conditions under which the pair-cascade can efficiently occur.