# Effects of Inner Alfv\'en Surface Location on Black Hole Energy Extraction in the Limit of a Force-Free Magnetosphere

## TL;DR

This study investigates how the position of the inner Alfvén surface influences the structure and energy extraction mechanisms of black hole magnetospheres in the force-free limit, revealing two main classes with different energy transmission characteristics.

## Contribution

It provides a comprehensive numerical analysis of magnetospheres with varying Alfvén surface locations, highlighting their impact on energy extraction and jet formation near black holes.

## Key findings

- Jet-like structures form near the horizon for Alfvén surfaces close to the ergosphere boundary.
- Energy is directed towards the equatorial plane when the Alfvén surface is near the horizon.
- Different Alfvén surface locations may lead to distinct observational signatures in high-energy phenomena.

## Abstract

An energy extracting black hole magnetosphere can be defined by the location of its inner Alfv\'{e}n surface, which determines the rate of black hole energy extraction along a given magnetic field line. We study how the location of the inner Alfv\'{e}n 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 Alfv\'{e}n surfaces near the boundary of the ergosphere and that energy is extracted towards the equatorial plane for Alfv\'{e}n 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 timescale by a factor of 20 or more.