  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.
