Abstract
ABSTRACT 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 q0 = 2aB0, 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 q0 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.
Highlights
Komissarov & McKinney (2007) attributed the effect of pulling the magnetic field lines back onto the black hole (BH) event horizon in their force-free simulations to the plasma conductivity, namely to the pinching of the axial poloidal electric current, but our results show that a finite BH charge may well be another reason
It may change some details of the magnetospheric dynamics but it cannot negate the gravitationally induced electric field and cannot result in a dead magnetosphere
Our results agree with the Wald’s conclusion that, BHs may acquire electric charge when placed into magnetic field of external origin
Summary
Even if such magnetosphere is filled with e−−e+ pairs via the two-photon process involving high-energy photons emitted by the accretion disk and its This conclusion was emphasised by King & Pringle (2021), who pointed that once the critical charge is reached, the electromagnetic potential is given by the same 4-vector equation as in the Wald solution for uncharged non-rotating BH. The conclusions by Wald (1974) and King & Pringle (2021) is in conflict with numerous MHD and force-free simulations of black hole magnetospheres, as well as with the few recent PIC simulations (Parfrey et al 2019; Crinquand et al 2020) It is in conflict with the theoretical analysis by Komissarov (2004) which shows that the gravitationally induced electric field of any steadystate axisymmetric BH magnetosphere cannot be screened provided the magnetosphere has no poloidal electric current.
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