Ultra-fast growth of primordial black holes through radiative absorption

Abstract

We show that Schwarzschild primordial black holes (PBHs) formed in the radiation-dominated era can grow extremely rapidly through $\textit{radiative absorption}$ governed by the full Stefan-Boltzmann law. By introducing a principle of isonomy - ensuring identical particle species dependence for Hawking emission and absorption - we find that, whenever the temperature of the PBH environment is larger than the PBH horizon temperature, PBHs generically gain mass. In particular, for PBH masses following the critical collapse mass-scaling law with critical exponent $γ_\mathrm{crit}$, with $γ_\mathrm{crit} \in (0.33, 0.49)$, the aforementioned radiative absorption mass growth mechanism produces a striking effect: PBHs forming with a mass $10^6M_\odot$ during BBN can reach $\mathcal{O}(10^{10} M_\odot)$ within $\mathcal{O}(10^{6} \mathrm{s})$ ($\sim $ 58 days). Interestingly enough, small deviations from $γ_\mathrm{crit}$, depending itself on the number of relativistic species present in the primordial plasma, yield a continuous PBH mass spectrum providing us ultimately with a single, Standard-Model-based explanation for the origin of stellar-mass, intermediate-mass, and supermassive black holes (SMBHs), and naturally accounting for the early appearance of SMBHs. The Schwarzschild treatment presented here can be extended to spherically symmetric cosmological black holes, indicating that radiative absorption is a dominant and previously overlooked PBH growth channel in the early Universe.

Figures (3)

• Figure 1: The critical value of the critical exponent $\gamma$ at which $M_\mathrm{f}\to \infty$ as a function of the temperature of the primordial thermal bath at the initial PBH formation time.
• Figure 2: The ratio $M_\mathrm{f}/M_\mathrm{i}$ as a function of $t/t_\mathrm{i}$ for different values of $\gamma$ in the vicinity of $\gamma_\mathrm{crit}$ for $M_\mathrm{i}=10^{27}\mathrm{g}$.
• Figure 3: The ratio $M_\mathrm{f}/M_\mathrm{i}$ as a function of $t$ for $M_\mathrm{i} = 10^{27}\mathrm{g}$ and $\gamma = 0.36191$ (blue curve) and $M_\mathrm{i} = 10^{6}M_\odot$ and $\gamma = 0.48554$ (red curve) accounting fully for the change of the relativistic degrees of freedom as temperature drops.