# Expanded solutions of force-free electrodynamics on general Kerr black holes

## TL;DR

This paper derives expanded solutions for force-free magnetospheres around Kerr black holes using a radial expansion method, identifying solutions that satisfy boundary conditions at the horizon and infinity, and improving their physical properties.

## Contribution

It introduces a radial expansion approach to extend known solutions of force-free electrodynamics on Kerr black holes, addressing their physical limitations.

## Key findings

- Extended solutions exhibit magnetic domination.
- Solutions have mostly timelike currents for certain parameters.
- The method improves the physical plausibility of existing solutions.

## Abstract

In this work, expanded solutions of force-free magnetospheres on general Kerr black holes are derived through a radial distance expansion method. From the regular conditions both at the horizon and at spatial infinity, two previously known asymptotical solutions (one of them is actually an exact solution) are identified as the only solutions that satisfy the same conditions at the two boundaries. Taking them as initial conditions at the boundaries, expanded solutions up to the first few orders are derived by solving the stream equation order by order. It is shown that our extension of the exact solution can (partially) cure the problems of the solution: it leads to magnetic domination and a mostly timelike current for restricted parameters.