General relativistic MHD simulations of monopole magnetospheres of black holes

In this paper we report the results of the first ever time-dependent general relativistic magnetohydrodynamic simulations of the magnetically dominated monopole magnetospheres of black holes. It is found that the numerical solution evolves towards a stable steady-state solution which is very close to the corresponding force-free solution found by Blandford and Znajek. Contrary to the recent claims, the particle inertia does not become dynamically important near the event horizon and the force-free approximation provides a proper framework for magnetically dominated magnetospheres of black holes. For the first time, our numerical simulations show the development of an ultra-relativistic particle wind from a rotating black hole. However, the flow remains Poynting dominated all the way up to the fast critical point. This suggests that the details of the so-called ``astrophysical load'', where the electromagnetic energy is transferred to particles, may have no effect on the efficiency of the Blandford-Znajek mechanism.