Magnetosphere of a Kerr black hole immersed in magnetized plasma and its perturbative mode structure

Abstract

This work studies jet-like electromagnetic configurations surrounding a slowly-spinning black-hole immersed in a uniformly magnetized force-free plasma. In the first part of this work, we present a family of stationary solutions that are jet-capable. While these solutions all satisfy the force-free equations and the appropriate boundary conditions, our numerical experiments show a unique relaxed state starting from different initial data, and so one member of the family is likely preferred over the others. In the second part of this work, we analyze the perturbations of this family of jet-like solutions, and show that the perturbative modes exhibit a similar split into the trapped and traveling categories previously found for perturbed Blandford-Znajek solutions. In the eikonal limit, the trapped modes can be identified with the fast magnetosonic waves in the force-free plasma and the traveling waves are essentially the Alfven waves. Moreover, within the scope of our analysis, we have not seen signs of unstable modes at the light-crossing timescale of the system, within which the numerical relaxation process occurs. This observation disfavors mode instability as the selection mechanism for picking out a preferred solution. Consequently, our analytical study is unable to definitively select a particular solution out of the family to serve as the aforementioned preferred final state. This remains an interesting open problem.