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.

Figures (2)

• Figure 1: Schematic of a Hawking–radiation–triggered ignition cascade. Micro–PBHs emit short HR bursts (blue arrows) that deposit energy within a causal patch (orange shell), tipping nearby near-threshold patches to collapse and creating new micro–PBHs, that launch further bursts and finally evaporate to non-emitting PMRs. Bottom: rescaled PBH density across the ignition front, which propagates with speed $v_f$ and has thickness $\ell_f$. (Not to scale.)
• Figure 2: Stochastic background from HR–ignited fronts: causal $f^{3}$ rise, flat plateau of height $h^{2}\Omega_{\rm pk}$, and UV fall $\propto f^{-2}$. Two benchmark spectra are shown: Case A (solid red) and Case B (dotted blue). Horizontal lines show the CMB–based $\Delta N_{\rm eff}$ cap (A: red dashed; B: blue dotted), and the shaded band marks the excluded region. Inset: Fisher–KPP ignition selects a pulled traveling front. Starting from a steep profile with localized bumps, diffusion and growth erase small–scale structure and the front converges to speed $v_c$ and width $\ell_f$.