  When a black hole accretes plasmas at very low accretion rate, an
advection-dominated accretion flow (ADAF) is formed. In an ADAF, relativistic
electrons emit soft gamma-rays via Bremsstrahlung. Some MeV photons collide
with each other to materialize as electron-positron pairs in the magnetosphere.
Such pairs efficiently screen the electric field along the magnetic field
lines, when the accretion rate is typically greater than 0.03-0.3% of the
Eddington rate. However, when the accretion rate becomes smaller than this
value, the number density of the created pairs becomes less than the
rotationally induced Goldreich-Julian density. In such a charge-starved
magnetosphere, an electric field arises along the magnetic field lines to
accelerate charged leptons into ultra-relativistic energies, leading to an
efficient TeV emission via an inverse-Compton (C) process, spending a portion
of the extracted hole's rotational energy. In this review, we summarize the
stationary lepton accelerator models in black hole magnetospheres. We apply the
model to super-massive black holes and demonstrate that nearby low-luminosity
active galactic nuclei are capable of emitting detectable gamma-rays between
0.1 and 30 TeV with the Cherenkov Telescope Array.
