  We examine the temporary evolution of axisymmetric magnetospheres around
rapidly rotating black holes (BHs), by applying our two-dimensional
particle-in-cell simulation code. Assuming a stellar-mass BH, we find that the
created pairs fail to screen the electric field along the magnetic field,
provided that the mass accretion rate is much small compared to the Eddington
limit. Magnetic islands are created by reconnection near the equator and
migrate toward the event horizon, expelling magnetic flux tubes from the BH
vicinity during a large fraction of time. When the magnetic islands stick to
the horizon due to redshift and virtually vanish, a strong magnetic field
penetrates the horizon, enabling efficient extraction of energy from the BH.
During this flaring phase, a BH gap appears around the inner light surface with
a strong meridional return current toward the equator within the ergosphere. If
the mass accretion rate is 0.025 percent of the Eddington limit, the BH's
spin-down luminosity becomes 16-19 times greater than its analytical estimate
during the flares, although its long-term average is only 6 percent of it. We
demonstrate that the extracted energy flux concentrates along the magnetic
field lines threading the horizon in the middle latitudes. It is implied that
this meridional concentration of the Poynting flux may result in the formation
of limb-brightened jets from low-accreting BH systems.
