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.
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