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We investigate the dynamics and emission of a starved magnetospheric region(gap) formed in the vicinity of a Kerr black hole horizon, using a new, fullygeneral relativistic particle-in-cell code that implements Monte Carlo methodsto compute gamma-ray emission and pair production through the interaction ofpairs and gamma rays with soft photons emitted by the accretion flow. It isfound that when the Thomson length for collision with disk photons exceeds thegap width, screening of the gap occurs through low-amplitude, rapid plasmaoscillations that produce self-sustained pair cascades, with quasi-stationarypair and gamma-ray spectra, and with a pair multiplicity that increases inproportion to the pair production opacity. The gamma-ray spectrum emitted fromthe gap peaks in the TeV band, with a total luminosity that constitutes afraction of about $10^{-5}$ of the corresponding Blandford-Znajek power. Thisstage is preceded by a prompt discharge phase of duration $\sim r_g/c$, duringwhich the potential energy initially stored in the gap is released as a flareof curvature TeV photons. We speculate that the TeV emission observed in M87may be produced by pair discharges in a spark gap.

Particle-in-cell simulations of pair discharges in a starved magnetosphere of a Kerr black hole