  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.
