Screw instability and the Blandford-Znajek mechanism

When magnetic field lines thread a rotating black hole's horizon and connec t with remote astrophysical loads, the rotational energy of the black hole can be extracted through the Blandford-Znajek mechanism. Due to the rotatio n of the black hole, the magnetic field lines are twisted and toroidal comp onents are generated. Thus, poloidal electric currents are induced and the black hole's rotational energy is transported to the astrophysical loads th rough Poynting flux. The Blandford-Znajek mechanism has been considered to be a possible process for powering extragalactic jets. In this Letter, we s how that because of the screw instability of the magnetic field, the toroid al components of the magnetic field, and thus the poloidal currents, cannot exceed the limits given by the Kruskal-Shafranov criterion. This significa ntly 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 ef ficiently within the neighborhood of the black hole. The implications of th e results for the scenario of extragalactic jets powered by the Blandford-Z najek mechanism are discussed.