On the mechanism of black hole energy reduction in the Blandford-Znajek process

The Blandford-Znajek (BZ) process is steady electromagnetic energy release from rotating black holes (BHs) along magnetic field lines threading them and widely believed to drive relativistic jets. This process is successfully demonstrated in general relativistic magnetohydrodynamic (MHD) simulations with the coordinate system regular on the event horizon, in which the outward Poynting flux on the horizon is considered to reduce BH energy. Meanwhile, alternative pictures for the BH energy reduction that invoke infall of negative energy objects were also discussed, although all of the proposed definitions of the negative energy and/or its infall velocity were ambiguous. We revisit the mechanism of BH energy reduction in the BZ process under the ideal MHD condition by utilizing the coordinate system singular on the horizon, in which the falling membrane of past accreted matter should exist above the horizon. We find that the Poynting flux is produced at the boundary between the falling membrane and the magnetically-dominated inflow, and the front of the inflow creates the negative electromagnetic energy, which reduces the rotational energy of spacetime. We also clarify that the poloidal electric current does not form a closed circuit within the magnetically-dominated flow. Previous interpretations of the BZ process and possibilities of violation of ideal MHD condition and BH charging are also discussed.