  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.
