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 the gap resides around the null charge surface
formed by the frame-dragging effect if there is no current injection
across the gap boundaries, and that it shifts outwards if a current
is injected across the inner boundary.
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 predicted that the VHE spectrum extends into higher energies
with increasing VHE photon flux.