Impact of general relativistic accretion on primordial black holes

Abstract

We demonstrate that general relativistic corrections to the accretion of relativistic matter onto primordial black holes (PBHs) can significantly enhance their mass growth during the early Universe. Contrary to previous Newtonian treatments, our analysis reveals that PBH masses can increase by an order of magnitude before evaporation, leading to substantial modifications of their lifetime and cosmological imprints. We quantify the resulting shifts in the minimum PBH mass constrained by Big Bang Nucleosynthesis (BBN), the revised lower bound for PBHs surviving today, and the dark matter parameter space allowed by PBH evaporation. Furthermore, we show that the enhanced accretion alters the high-frequency gravitational wave spectrum from PBH evaporation, potentially within the reach of future detectors. Our results provide a comprehensive, relativistically consistent framework to delineate the role of PBHs in early-universe cosmology and dark matter phenomenology.

Figures (6)

• Figure 1: Plot of flow velocity ($v$) as a function of radial distance ($r$) for different accretion rate, with an equation of state $\omega=1/3$.
• Figure 2: PBH mass ($M$) evolution as a function of scale factor ($a$) for initial masses of $10$ g (dashed) and $10^8$ g (solid), comparing relativistic (green) and non-relativistic (red) accretion along with Hawking evaporation.
• Figure 3: Initial PBH mass ($M_{\rm in}$) as a function of evaporation temperature ($T_{\rm ev}$), shown for three cases namely, blue, red, and green curves representing without, with non-relativistic, and with relativistic accretion respectively.
• Figure 4: Variation of $\beta$ with $M_{\rm in}$ for various DM masses. Dotted lines represent scenarios with only Hawking evaporation, while the solid lines incorporate the effects of relativistic accretion as well. Shaded regions indicate constraints from inflation (light blue), BBN (green), improved BBN (light green), and Ly-$\alpha$ limits (yellow line).
• Figure 5: Constraints on the PBH dark matter fraction $f_{\rm PBH}$ vs. initial mass $M_{\rm in}$ are shown. The dashed curve includes only Hawking evaporation; the solid curve also accounts for relativistic accretion. Shaded regions denote bounds from evaporation (red), microlensing (blue), and GWs (purple). Black lines mark the critical mass with (solid) and without (dashed) accretion.