Force-Free Electrodynamics around Extreme Kerr Black Holes

TL;DR

This paper derives exact analytical solutions for the highly nonlinear force-free electrodynamics equations near the horizon of a maximally spinning black hole, revealing symmetries that enable solutions previously accessible only numerically.

Contribution

It introduces a novel analytical approach leveraging conformal symmetry to solve the nonlinear FFE equations near extremal Kerr black holes.

Findings

Derived infinite families of exact solutions

Revealed enhanced conformal symmetry in the near-horizon region

Provided insights into energy extraction mechanisms

Abstract

Plasma-filled magnetospheres can extract energy from a spinning black hole and provide the power source for a variety of observed astrophysical phenomena. These magnetospheres are described by the highly nonlinear equations of force-free electrodynamics, or FFE. Typically these equations can only be solved numerically. In this paper we consider the FFE equations very near the horizon of a maximally spinning black hole, where the energy extraction takes place. Thanks to an enhanced conformal symmetry which appears in this near-horizon region, we are able to analytically obtain several infinite families of exact solutions of the full nonlinear equations.