Peculiar Black-Hole Unipolar Induction

Abstract

It is argued that a posteriori without conflicting with the dubbed no-hair theorem, a Kerr black hole acquires its own proper magnetosphere in the steady eigen-state. The angular frequency of field lines, $ {\Omega_{\rm F}}$ , given as the eigenvalue in terms of the hole’s angular frequency, $ {\Omega_{\rm H}}$ , couples with the frame-dragging angular frequency, $ \omega$ , to create an inner general-relativistic domain of $ {\Omega_{\rm H}} \gt \omega$$ \gt {\Omega_{\rm F}}$ , in which the gradient of the electric potential is, when viewed by the fiducial observers (FIDOs), reversed in direction from that in the outer quasi-classical domain of $ {\Omega_{\rm F}} \gt \omega$$ \gt$ 0. The field lines are pinned down in the plasma source at the interface between the two domains (upper null surface S$ _{\rm N}$ ), from which pair-particles well up, charge-separated into the ingoing and outgoing winds. The EMFs due to unipolar induction operate to drive the surface currents, following Ohm’s law, on the resistive membranes terminating the force-free domains (say, S$ _{\rm ffH}$ and S$ _{{\rm ff}\infty}$ ), to exert the surface torques onto the respective membranes, thereby extracting angular momentum from the hole and transferring to the domain of astrophysical loads.