Electrodynamics of black hole magnetospheres

TLDR: In this paper, a 3 + 1 system of equations for the Blandford-Znajek mechanism was proposed, which not only has a more traditional form than the now classic 3+1 system of Thorne and Macdonald but also is more general.

Abstract: The main goal of this research is to get better insights into the properties of the plasma-filled magnetospheres of black holes by means of direct numerical simulations and, ultimately, to resolve the controversy surrounding the Blandford-Znajek mechanism. Driven by the need to write the equations of black hole electrodynamics in a form convenient for numerical applications, we constructed a new system of 3 + 1 equations, which not only has a more traditional form than the now classic 3 + 1 system of Thorne and Macdonald but also is more general. To deal with the magnetospheric current sheets, we also developed a simple model of radiative resistivity based on the inverse Compton scattering of background photons. The results of numerical simulations combined with simple analytical arguments allow us to make 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 magnetohydrodynamic 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 also 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.