  We investigate the temporal evolution of an axisymmetric magnetosphere around
a rapidly rotating, stellar-mass black hole, applying a two-dimensional
particle-in-cell simulation scheme. Adopting a homogeneous pair production, and
assuming that the mass accretion rate is much less than the Eddington limit, we
find that the black hole's rotational energy is preferentially extracted from
the middle latitudes, and that this outward energy flux exhibits an enhancement
that lasts approximately 160 dynamical time scales. It is demonstrated that the
magnetohydrodynamic approximations cannot be justified in such a
magnetically-dominated magnetosphere, because the Ohm's law completely breaks
down, and because the charge-separated electron-positron plasmas are highly
non-neutral. An implication is given regarding the collimation of relativistic
jets.
