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 (IC) 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. plasma accretion toward the rotation axis, the magnetic energy density dominates the plasmas' rest-mass energy density in these polar funnels.Within such a nearly vacuum, polar funnel, electron-positron pairs are supplied via the collisions of MeV photons emitted from the equatorial, accreting region. For example, when the mass accretion rate is typically less than 1% of the Eddington rate, the accreting plasmas form an advection-dominated accretion flow (ADAF), emitting radio to infrared photons via the synchrotron process and MeV photons via free-free and inverse-Compton (IC) processes [28,29]. Particularly, when the accretion rate becomes much less than the Eddington rate, the ADAF MeV photons can no longer sustain a force-free magnetosphere, which inevitably leads to the appearance of an electric field, E‖, along the magnetic field lines in the polar funnel. In such a vacuum gap, we can expect that the BZ power may be partially dissipated as particle acceleration and emission near the central engine, in the same manner as in pulsar outer gap (OG) model. In what follows, we summarize this vacuum gap model in BH magnetospheres.
The Pulsar Outer Gap ModelThe Large Area Telescope (LAT) aboard the Fermi space gamma-ray observatory has detected pulsed signals in high-energy (HE) (0.1 GeV-10 GeV) gamma-rays from more than 200 rotation-powered pulsars [30]. Among them, 20 pulsars exhibit pulsed signals above 10 GeV, including 10 pulsars up to 25 GeV and other 2 pulsars above 50 GeV. Moreover, more than 99% of the LAT-detected young and millisecond pulsars exhibit phase-averaged spectra that are consistent with a pure-exponential or a sub-exponential cut off above the cutoff energies at a few GeV. What is more, 30% of these young pulsars show sub-exponential cut off, a slower decay than t...