Towards an understanding of the force-free magnetosphere of rapidly spinning black holes

TL;DR

This paper explores analytical solutions for the force-free magnetosphere around rapidly spinning black holes, focusing on the near horizon region's enhanced symmetry to simplify complex equations.

Contribution

It introduces a novel approach to derive physically meaningful solutions for the force-free equations in the NHEK region, advancing understanding of black hole magnetospheres.

Findings

Reduction of force-free equations to a single nonlinear ODE

Development of a new method for obtaining solutions

Enhanced understanding of magnetosphere structure near extremal Kerr black holes

Abstract

The ability of a plasma surrounding spinning black holes to extract rotational energy and power energetic emissions has been recognized as a key astrophysical phenomenon. Important insights into the nature of this process are obtained through the analysis of the interplay between a force-free magnetosphere and the black hole. This task involves solving a complicated system of equations, often requiring complex numerical simulations. Recent analytical attempts at tackling this problem have exploited the fact that the near horizon region of extreme Kerr (NHEK) is endowed with an enhanced symmetry group. We continue in this direction and show that for some conformally self-similar solutions, the NHEK force-free equations reduce to a single non-linear ordinary differential equation which is difficult to solve with straightforward integration. We here introduce a new approach specifically tailored to this problem and describe how one can obtain physically meaningful solutions.