  We investigate the electrostatic acceleration of electrons and positrons in
the vicinity of the event horizon, applying the pulsar outer-gap model to black
hole magnetospheres. During a low accretion phase, the radiatively inefficient
accretion flow (RIAF) cannot emit enough MeV photons that are needed to sustain
the force-free magnetosphere via two-photon collisions. In such a
charge-starved region (or a gap), an electric field arises along the magnetic
field lines to accelerate electrons and positrons into ultra-relativistic
energies. These relativistic leptons emit copious gamma-rays via curvature and
inverse-Compton (IC) processes. Some of such gamma-rays collide with the
submillimeter-IR photons emitted from the RIAF to materialize as pairs, which
polarize to partially screen the original acceleration electric field. It is
found that the gap gamma-ray luminosity increases with decreasing accretion
rate. However, if the accretion rate decreases too much, the diminished RIAF
soft photon field can no longer sustain a stationary pair production within the
gap. As long as a stationary gap is formed, the magnetosphere becomes
force-free outside the gap by the cascaded pairs, irrespective of the BH mass.
If a nearby stellar-mass black hole (BH) is in quiescence, or if a galactic
intermediate-mass BH is in a very low accretion state, its curvature and IC
emissions are found to be detectable with Fermi/LAT and imaging atmospheric
Cherenkov telescopes (IACT). If a low-luminosity active galactic nucleus is
located within a few tens of Mpc, the IC emission from its super-massive BH is
marginally detectable with IACT.
