Electromagnetic Extraction of Energy from Kerr Black Holes

The energy extraction process from Kerr black holes is elucidated compared with that from pulsars in force-free degenerate electrodynamics (FFDE). It is argued for the force-free magnetosphere of a Kerr black hole in a steady axisymmetric state that the function of unipolar inductors in the presence of global magnetic fluxes threading the horizon is equipped by a frame-dragging effect in the Kerr spacetime metric to the upper null surface, $\mathrm{S}_{\mathrm{N}}$ , with the axial distance, $\varpi_{\mathrm{N}}$ , where the local value of the angular velocity of the frame-dragging, $\omega$ , is equal to the rotational frequency of each field line, i.e., $\omega(\varpi_{\mathrm{N}}) = \Omega_{\mathrm{F}}$ , and the rotational velocity of each field line, $\boldsymbol{v}_{\mathrm{F}}$ , measured by “zero-angular-momentum-observers” changes in sign. There must be a pair-creation gap at $\mathrm{S}_{\mathrm{N}}$ , from which the paired winds, ingoing and outgoing, are initiated. The poloidal electric current, $I$ , for each wind is determined by solving the eigenvalue problem with the “criticality condition” imposed at the fast surfaces nearly at the horizon and at infinity, and the “current-closure condition” at $\mathrm{S}_{\mathrm{N}}$ determines the ultimate eigenvalues of $\Omega_{\mathrm{F}}$ and $I$ in terms of the hole’s angular velocity, $\Omega_{\mathrm{H}} = \omega(r_{\mathrm{H}})$ , and the distribution of the magnetic flux at the horizon. It is not in the ordinary ergosphere, but in the effective ergosphere in the region of $\Omega_{\mathrm{H}} \gt \omega \gt \Omega_{\mathrm{F}}$ and $\boldsymbol{v}_{\mathrm{F}}