  The Blandford-Znajek process, the steady electromagnetic energy extraction
from a rotating black hole, is widely believed to work for driving relativistic
jets, although it is still under debate where the electric current is driven.
We address this issue analytically by investigating the time-dependent state in
the Boyer-Lindquist and Kerr-Schild coordinate systems. This analysis suggests
that a non-ideal magnetohydrodynamic region is required in the time-dependent
state, while not in the steady state.
