  It is argued that the zero-angular-momentum-observers (ZAMOs) circulating
with the frame-dragging-angular-velocity $\omega$ plays a leading part in
energy extraction. When the condition $\Omega_{\rm F}<\Omega_{\rm H}$ is
satisfied, where $\Omega_{\rm H}$ and $\Omega_{\rm F}$ are the horizon and
field-line (FL) angular-velocities (AVs), they will see that the null surface
S$_{\rm N}$ with $\omega_{\rm N}=\Omega_{\rm F}$ always exists in the
force-free magnetosphere. The pivotal ZAMO-measured FLAV $\Omega_{\rm ZF}
\equiv \Omega_{\rm F} - \omega$ changes sign on this surface S$_{\rm N}$ where
the force-free and freezing-in conditions break down. The force-free
magnetosphere is divided on this surface, with particle-current sources on it.
The outer domain ${D}_{\rm (out)}$ outside S$_{\rm N}$ spins forward
($\Omega_{\rm ZF}>0$), whereas the inner domain ${D}_{\rm (in)}$ inside spins
backward ($\Omega_{\rm ZF}<0$).
  Because the electric field ${\bf E}_{\rm p}$ reverses direction there, the
Poynting flux reverses direction as well from outward to inward, though the
positive angular momentum always flows outwardly.
  Electromagnetic self-extraction of energy will be possible only through the
frame-dragged magnetosphere, with the inner domain ${D}_{\rm (in)}$ nested
between the horizon and the surface S$_{\rm N}$, when $\Omega_{\rm
F}<\Omega_{\rm H}$ is ensured by the 1st and 2nd laws of thermodynamics.
