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

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, fully general relativistic particle-in-cell code that implements Monte Carlo methods to compute gamma-ray emission and pair production through the interaction of pairs and gamma rays with soft photons emitted by the accretion flow. It is found that when the Thomson length for collision with disk photons exceeds the gap width, screening of the gap occurs through low-amplitude, rapid plasma oscillations that produce self-sustained pair cascades, with quasi-stationary pair and gamma-ray spectra, and with a pair multiplicity that increases in proportion to the pair production opacity. The gamma-ray spectrum emitted from the gap peaks in the TeV band, with a total luminosity that constitutes a fraction of about 10^-5 of the corresponding Blandford-Znajek power. This stage is preceded by a prompt discharge phase of duration ∼r_g/c, during which the potential energy initially stored in the gap is released as a flare of curvature TeV photons. We speculate that the TeV emission observed in M87 may be produced by pair discharges in a spark gap.