Electrically charged black holes and the Blandford-Znajek mechanism

Recently, it was claimed by King & Pringle that accretion of electric charge by a black hole (BH) rotating in an aligned external magnetic field results in a 'dead' vacuum magnetosphere, where the electric field is totally screened, no vacuum breakdown is possible, and the Blandford-Znajek mechanism cannot operate. Here, we study in details the properties of the Wald solution for electrically charged BHs discussed in their paper. Our results show that the claim is erroneous as in the solution with the critical charge q(0) = 2aB(0), there exists a drop of electrostatic potential along all magnetic field lines except the one coinciding with the symmetry axis. It is also found that while uncharged rotating BHs expel external vacuum magnetic field from their event horizon (the Meissner effect), electric charging of BHs pulls the magnetic field lines back on it, resembling what has been observed in some previous force-free, Relativistic Magnetohydrodynamics (RMHD), and Particle-in-Cell (PIC) simulations of BH magnetospheres. This suggests that accretion of electric charge may indeed be a feature of the BH electrodynamics. However, our analysis shows that the value q(0) of the BH charge given by Wald is likely to be only an upper limit, and that the actual value depends of the details of the magnetospheric physics.