# Perturbing Monopolar Force-Free Magnetospheres to Slowly Rotating Black Holes

## TL;DR

This paper investigates how frame-dragging influences force-free magnetospheres around slowly rotating black holes, revealing a bifurcation in magnetic field configurations due to perturbations in black hole spin.

## Contribution

It demonstrates that the common perturbed monopolar solution acts as a separatrix between two distinct classes of magnetic field structures influenced by frame-dragging effects.

## Key findings

- Perturbed monopolar solutions separate two magnetic field configurations.
- Frame-dragging alters toroidal magnetic fields and force balance.
- Magnetic field lines bend differently depending on solution class.

## Abstract

We study the effects of frame-dragging on the structure of force-free magnetospheres around rotating black holes. For slowly rotating black holes, analytic explorations often focus on transforming an exact force-free solution applicable to a static black hole into a solution approximately applicable to a slowly-rotating black hole via perturbations in black hole spin. We show that the single perturbed monopolar solution most commonly arrived at using such techniques is in fact a separatrix between two broad classes of solutions: those with poloidal magnetic fields that bend upwards towards the azimuthal axis and those that bend downwards towards the equatorial plane. This is because frame-dragging affects the toroidal magnetic field distributions, changing the force balance between poloidal magnetic field lines.