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 holes 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.
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