Screw Instability and Blandford-Znajek Mechanism

When magnetic field lines thread a rotating black hole's horizon and connect with remote astrophysical loads, the rotational energy of the black hole can be extracted through the Blandford-Znajek mechanism. Due to the rotation of the black hole, the magnetic field lines are twisted and toroidal components are generated. So poloidal electric currents are induced and the black hole's rotational energy is transported to the astrophysical loads through Poynting flux. The Blandford-Znajek mechanism has been considered to be a possible process for powering extragalactic jets. In this paper we show that due to the screw instability of magnetic field, the toroidal components of the magnetic field, and thus the poloidal currents, cannot exceed the limits given by the Kruskal-Shafranov criterion. This significantly lowers the power of the Blandford-Znajek mechanism when the loads are far from the black hole. So the Blandford-Znajek mechanism can only work efficiently within the neighborhood of the black hole. The implications of the results for the scenario of extragalactic jets powered by the Blandford-Znajek mechanism are discussed.