Effects of inner Alfvén surface location on black hole energy extraction in the limit of a force-free magnetosphere

An energy-extracting black hole magnetosphere can be defined by the location of its inner Alfvén surface, which determines the rate of black hole energy extraction along a given magnetic field line. We study how the location of the inner Alfvén surface can modify the structure of energy-extracting black hole magnetospheres in the force-free limit. Hundreds of magnetospheres are numerically computed via a general-relativistic extension of the Newtonian magnetofrictional method for a full range of black hole spins and flow parameters. We find that jet-like structures naturally form very close to the horizon for Alfvén surfaces near the boundary of the ergosphere and that energy is extracted towards the equatorial plane for Alfvén surfaces close to the horizon. This suggests that two broad classes of energy-extracting black hole magnetospheres might exist: those that transmit extracted energy directly to distant observers, and those that transmit extracted energy to nearby accreting matter. Applied to transient high-energy phenomena, we find that they might also differ in time scale by a factor of 20 or more.