The Force-Free Magnetosphere of a Rotating Black Hole

TL;DR

This paper solves the steady-state force-free magnetosphere structure around a Kerr black hole, confirming energy extraction rates and exploring magnetic field configurations crossing critical surfaces.

Contribution

It provides a self-consistent solution for the magnetosphere structure around a Kerr black hole using a numerical iterative method for the split monopole configuration.

Findings

Confirmed the electromagnetic energy extraction rate matches previous results.

Demonstrated the solution's dependence on magnetic field angular velocity and electric current distributions.

Discussed the physical relevance of magnetic configurations crossing light surfaces.

Abstract

We revisit the Blandford & Znajek (1977) process and solve the fundamental equation that governs the structure of the steady-state force-free magnetosphere around a Kerr black hole. The solution depends on the distributions of the magnetic field angular velocity omega and the poloidal electric current I. These are not arbitrary. They are determined self-consistently by requiring that magnetic field lines cross smoothly the two singular surfaces of the problem, the inner `light surface' located inside the ergosphere, and the outer `light surface' which is the generalization of the pulsar light cylinder. We find the solution for the simplest possible magnetic field configuration, the split monopole, through a numerical iterative relaxation method analogous to the one that yields the structure of the steady-state axisymmetric force-free pulsar magnetosphere (Contopoulos, Kazanas & Fendt 1999). We obtain the rate of electromagnetic extraction of energy and confirm the results of Blandford and Znajek and of previous time dependent simulations. Furthermore, we discuss the physical applicability of magnetic field configurations that do not cross both `light surfaces'.