We search for the gamma-ray counterparts of stellar-mass black holes using long-term Fermi archive to investigate the electrostatic acceleration of electrons and positrons in the vicinity of the event horizon, by applying the pulsar outer-gap model to their magnetosphere. When a black hole transient (BHT) is in a low-hard or quiescent state, the radiatively inefficient accretion flow cannot emit enough MeV photons that are required to sustain the force-free magnetosphere in the polar funnel via two-photon collisions. In this charge-starved gap region, 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 the curvature and inverse-Compton (IC) processes. It is found that these gamma-ray emissions exhibit a flaring activity when the plasma accretion rate stays typically between 0.01 and 0.005 percent of the Eddington value for rapidly rotating, stellar-mass black holes. By analyzing the detection limit determined from archival Fermi/LAT data, we find that the 7-year averaged duty cycle of such flaring activities should be less than 5% and 10% for XTE J1118+480 and 1A 0620-00, respectively, and that the detection limit is comparable to the theoretical prediction for V404 Cyg. It is predicted that the gap emission can be discriminated from the jet emission, if we investigate the high-energy spectral behaviour or observe nearby BHTs during deep quiescence simultaneously in infrared wavelength and very-high energies.
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