Stability of Force-Free Magnetospheres

TL;DR

This paper investigates the stability and dynamical behavior of force-free magnetospheres around rotating black holes, identifying mode classifications and suggesting the stability of the Blandford-Znajek solution.

Contribution

It classifies electromagnetic perturbations into trapped modes and traveling waves, providing new insights into the stability and dynamics of black hole magnetospheres.

Findings

Blandford-Znajek solution is mode stable.

Electromagnetic perturbations split into trapped modes and traveling waves.

Traveling waves relate to no-scattering Poynting flux solutions.

Abstract

We analyze the dynamical evolution of a perturbed force-free magnetosphere of a rotating black hole, which is described by the Blandford-Znajek solution in the stationary limit. We find that the electromagnetic field perturbations can be classified into two categories: "trapped modes" and "traveling waves". The trapped modes are analogous to the vacuum (without plasma) electromagnetic quasinormal modes in rotating black hole spacetimes, but with different eigenfrequencies and wave functions, due to their coupling with the background electromagnetic field and current. The traveling waves propagate freely to infinity or the black hole horizon along specific null directions, and they are closely related to the no-scattering Poynting flux solutions discovered by Brennan, Gralla and Jacobson. Our results suggest that the Blandford-Znajek solution is mode stable, and more importantly we expect this study to illuminate the dynamical behavior of force-free magnetospheres as well as to shed light on the path to new exact solutions.