Electrodynamics of black hole magnetospheres
  Numerical simulations combined with simple analytical arguments are used to reach a number of important conclusions on the nature of the Blandford-Znajek mechanism. We show that, just like in the Penrose mechanism and in the MHD models of Punsly and Coroniti, the key role in this mechanism is played by the black hole ergosphere. The poloidal currents are driven by the gravitationally induced electric field which cannot be screened within the ergosphere by any static distribution of the electric charge of locally created pair plasma. Contrary to what is expected in the Membrane paradigm, the energy and angular momentum are extracted not only along the magnetic field lines penetrating the event horizon but along all field lines penetrating the ergosphere. In dipolar magnetic configurations symmetric relative to the equatorial plane the force-free approximation breaks down within the ergosphere where a strong current sheet develops along the equatorial plane. This current sheet supplies energy and angular momentum at infinity to the surrounding force-free magnetosphere. The Blandford-Znajek monopole solution is found to be asymptotically stable and causal. The so-called horizon boundary condition of Znajek is shown to be a regularity condition at fast critical surface. 
S. S. Komissarov