  Supermassive black holes are believed to be the central power house of active
galactic nuclei. Applying the pulsar outer-magnetospheric particle accelerator
theory to black-hole magnetospheres, we demonstrate that an electric field is
exerted along the magnetic field lines near the event horizon of a rotating
black hole. In this particle accelerator (or a gap), electrons and positrons
are created by photon-photon collisions and accelerated in the opposite
directions by this electric field, efficiently emitting gamma-rays via
curvature and inverse-Compton processes. It is shown that a gap arises around
the null charge surface formed by the frame-dragging effect, provided that
there is no current injection across the gap boundaries. The gap is dissipating
a part of the hole's rotational energy, and the resultant gamma-ray luminosity
increases with decreasing plasma accretion from the surroundings. Considering
an extremely rotating supermassive black hole, we show that such a gap
reproduces the significant very-high-energy (VHE) gamma-ray flux observed from
the radio galaxy IC 310, provided that the accretion rate becomes much less
than the Eddington rate particularly during its flare phase. It is found that
the curvature process dominates the inverse-Compton process in the
magnetosphere of IC~310, and that the observed power-law-like spectrum in VHE
gamma-rays can be explained to some extent by a superposition of the curvature
emissions with varying curvature radius. It is predicted that the VHE spectrum
extends into higher energies with increasing VHE photon flux.

High Energy Astrophysical Phenomena