Analytic properties of force-free jets in the Kerr spacetime- I

TL;DR

This paper develops a perturbation method to analyze force-free jets from the Blandford-Znajek mechanism in Kerr spacetime, providing accurate solutions for energy extraction and a key constraint for magnetic field configurations.

Contribution

It introduces a high-order perturbation solution for the BZ mechanism and derives an exact constraint for monopole magnetic fields in Kerr spacetime, aiding theoretical and numerical studies.

Findings

Accurate energy extraction rate for all black hole spins.

High-order perturbation solution describing BH magnetosphere.

Exact magnetic field constraint for benchmarking simulations.

Abstract

Blandford-Znajek (BZ) mechanism describes a process extracting rotation energy from a spinning black hole (BH) via magnetic field lines penetrating the event horizon of central BH. In this paper, we present a perturbation approach to study force-free jets launched by the BZ mechanism, and its two immediate applications: (1) we present a high-order split monopole perturbation solution to the BZ mechanism, which accurately pins down the energy extraction rate $\dot E$ and well describes the structure of BH magnetosphere for all range of BH spins ($0\leq a\leq 1$); (2) the approach yields an exact constraint for the monopole field configuration in the Kerr spacetime, $I = \Omega (1-A_\phi^2)$, where $A_\phi$ is the $\phi-$component of the vector potential of electromagnetic field, $\Omega$ is the angular velocity of magnetic field lines and $I$ is the poloidal electric current. The constraint is of particular importance to benchmark the accuracy of numerical simulations.