Direct numerical simulations of the Blandford-Znajek effect

The time-dependent general relativistic equations of degenerate electrodynamics are solved numerically in order to study the mechanism of the electromagnetic extraction of the rotational energy of black holes. We performed a series of 2D runs for black holes with specific angular momentum, a, from 0.1 to 0.9 and for a monopole magnetic field assuming axisymmetry. In the inner region of the wind, the solution quickly settles to a steady state with an outgoing Poynting flux. In all cases the angular velocity of the magnetic field lines is almost half the angular velocity of the black hole. Thus, at least for the configuration considered, the Blandford–Znajek mechanism operates near its maximum power output.