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 forcefree 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 Alfvén 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.

Magnetosphere of a spinning black hole and the role of the current sheet

“…In this work, we revisit this problem guided by high accuracy solutions, again obtained by evolving the general-relativistic force-free equations. We confirm previous results regarding the structure of the electromagnetic fields, the angular velocity, and luminosity from these solutions [2,[4][5][6][7]. However, we also focus on some new aspects.…”

“…Here we study a prototypical setup that exhibits the Blandford-Znajek mechanism: a spinning BH immersed in a uniformly magnetized plasma. Starting with [2], there have been a number of studies of this problem using numerical evolutions of the generalrelativistic equations of FFE [3][4][5][6][7]. These have found that the solution relaxes to a stationary BH jet configuration with a Poynting flux powered by the rotational energy of the BH.…”

“…In [6], a whole family of stationary BH jet solutions describing a slowly spinning BH in a uniformly magnetized plasma was presented. However, no sign of mode instability on the relevant time scales was found for these solutions (see also [8] for a study of the stability of Blandford-Znajek split-monopole type magnetosphere configurations), and it was left as an open question what condition picked out the unique solution found by the numerical evolutions.…”

Magnetosphere structure of a Kerr black hole: Marginally force-free equatorial boundary condition

“…But for the vertical field lines, their exists only one LS, which is insufficient for determining two eigenfunctions. In this case, many solutions are expected [15,16], but the many-solutions scenario is in conflict with several previous FFE simulations [5,[17][18][19][20][21][22]. To explain the discrepancy on the uniqueness of uniform field solution, Pan et al [23,24] proposed that the two eigenfunctions are not independent; instead, they are related by the radiation condition at infinity, which is formulated asÊ θ =B φ , withÊ θ andB φ being the θ component of electric field and φ component of the magnetic field measured by zero-angularmomentum-observers, respectively.…”

“…But for other magnetic field configurations, there is no such good agreement, e.g., different approaches do not even reach a consensus on the solution uniqueness for the uniform field configuration. Several force-free electrodynamics (FFE) simulations [5,[17][18][19][20][21][22] have been done and the BH magnetospheres in these simulations all settle down to a steady state with similar final field configuration, which is an indicator for solution uniqueness.…”