Electron-positron cascade in magnetospheres of spinning black holes

We study the magnetospheres of spinning black holes (BHs) in active Galactic Nuclei (AGN), quasars, blazars and such. It is believed that spinning BHs in ambient magnetic fields develop force-free magnetospheres. Their structure should determine how relativistic jets are launched and how the BH energy is extracted, e.g., via Blandford-Znajek mechanism. The key assumption for the force-free condition is the presence of plasma with the density being above the Goldreigh-Julian density. Unlike NSs which can in principle supply electrons from the surface, BH cannot supply plasma at all. The plasma must be generated {\it in situ} via an electron-positron cascade, presumably in the gap region. Here we study such pair cascade and find the conditions under which it can occur and, hence, AGN and quasar/blazar jets can exist.