# The Structure of Magnetically Dominated Energy Extracting Black Hole Magnetospheres: Dependencies on Field Line Angular Velocity

## TL;DR

This paper investigates how the angular velocity distribution of magnetic field lines influences the structure and energy output of magnetospheres around rotating black holes, revealing significant variability in energy flux.

## Contribution

It introduces a proxy for the inner light surface based on field line angular velocity and explores its impact on magnetosphere structure and energy extraction.

## Key findings

- Outward Poynting flux varies by over a factor of 100 with different field line angular velocities.
- Inner light surface must lie within the ergoregion for energy extraction.
- Magnetosphere structure is highly sensitive to the distribution of magnetic field line angular velocity.

## Abstract

If a magnetically dominated magnetosphere is to extract a black hole's rotational energy and transmit it to distant regions, then the inner light surface of that magnetosphere must lie within the ergoregion. That inner light surface condition limits the angular velocity of magnetic field lines. We take the distribution of magnetic field line angular velocity on the horizon to be a useful proxy for inner light surface location and study how different distributions affect the structure of energy-extracting magnetospheres. Within magnetospheres that exhibit differential field line bending towards both the azimuthal axis and the equatorial plane, we find that the total Poynting flux energy directed outward along the azimuthal axis can vary by over a factor of 100 for a single value of black hole spin.