Hawking-radiation-ignited autocatalytic formation of primordial black holes

Abstract: We propose and analyze an autocatalytic mechanism in which bursts of Hawking radiation from evaporating micro-primordial black holes (PBHs) trigger the collapse of near-critical plasma overdensities. In a primordial plasma seeded with such patches, this feedback self organizes into a traveling ignition front that successively forms new PBHs and then self-quenches as the Universe expands. A minimal reaction-diffusion model yields conservative criteria for ignition and freeze-out and predicts a stochastic gravitational-wave background with a sharp causal low-frequency edge set by the freeze-out correlation length and largely insensitive to Planck-scale PBH endpoint microphysics. The resulting sub-Hz-to-audio band and amplitudes satisfy cosmological energy-injection bounds, providing a clean, testable target for forthcoming gravitational-wave observatories.