Where is the electric current driven in the Blandford-Znajek process?

Abstract: 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.