We investigate the acceleration of electrons and positrons by magnetic-field-aligned electric fields in the polar funnel of an accreting black hole ( BH ) .
Applying the pulsar outer-gap theory to BH magnetospheres , we find that such a lepton accelerator arises in the immediate vicinity of the event horizon due to frame-dragging , and that their gamma-ray luminosity increases with decreasing accretion rate .
Furthermore , we demonstrate that the gamma-ray flux is enhanced along the rotation axis by more than an order of magnitude if the BH spin increases from a = 0.90 M to a = 0.9999 M .
As a result , if a ten-solar-mass , almost-maximally rotating BH is located within 3 kpc , when its accretion rate is between 0.005 % and 0.01 % of the Eddington rate , its high-energy flare becomes detectable with the Fermi/Large Area Telescope , provided that the flare lasts longer than 1.2 months and that we view the source nearly along the rotation axis .
In addition , its very-high-energy flux is marginally detectable with the Cherenkov Telescope Array , provided that the flare lasts longer than a night and that our viewing angle is about 45 degrees with respect to the rotation axis .