Trapped fireshell (halo) of photons and pairs around black-hole horizon: Source for ultra-high-energy particles

We study the Compton-rocket effect of strong radiation force accelerating electrons in an opaque fireshell (or fire spot) of dense photons and electron-positron pairs, whose temperature is spatially inhomogeneous and exceeds the electron mass. We find the possibility of the charged-particle acceleration and the avalanche runaway process, leading to a non-trivial probability of ultra-high-energy (UHE) electrons and protons, which subsequently produce very-high-energy (VHE) photons and neutrinos. In a simplified one-dimensional model, we qualitatively show such peculiar dynamics using the fireball, Gamma-Ray Burst central engine, whose inner part inflows and forms a gravitationally trapped fireshell (halo) around the horizon of a black hole. The fireshell is metastable, cooling via UHE particle emissions and blackbody radiation. We calculate the UHE particle luminosity varying in time, and discuss the peculiar features of such produced UHE particles, which lead to VHE particles, in connection with possible numerical simulations, observations and experiments.