Revisiting PBH Accretion, Evaporation and Their Cosmological Consequences

TL;DR

This work formulates a self-consistent, fully relativistic treatment of primordial black hole evolution by coupling Kerr BH accretion in a radiation-dominated universe to Hawking evaporation with spin-dependent greybody factors. The authors derive a spin-aware accretion efficiency $\lambda_{\text{Kerr}}(a_*)$, show that relativistic accretion significantly increases PBH masses while rapidly diluting spin, and demonstrate that PBHs effectively become Schwarzschild well before evaporation. These effects tighten BBN constraints by a factor of $\sim 4$–$5$, lower the mass required for survival to the present to $\sim 2.7\times10^{14}$ g, and shift the DM and SGWB phenomenology, notably erasing the high-frequency spin-induced SGWB feature. The results dramatically alter the mapping between initial PBH mass and present observables, reshaping the viable PBH DM parameter space and providing a distinct observational signature through the suppressed SGWB peak structure.

Abstract

Primordial black holes (PBHs) provide a unique probe of the early Universe. Their cosmological evolution is governed by the competition between mass accretion and Hawking evaporation. In this paper we look into the details impact of accretion. Most of the earlier analysis relied on non-relativistic accretion models. In this work, we reinvestigate this in a fully relativistic framework for Kerr PBHs in the radiation-dominated era. We derive relativistic accretion rate and compute spin-dependent efficiency $λ_{\text{Kerr}}(a_*)$. Using this result, we construct coupled evolution equations for the PBH mass and spin that include both relativistic accretion and spin-dependent evaporation. Our analysis shows that relativistic accretion significantly increases PBH masses and consequently suppresses their spins, causing all PBHs to become effectively Schwarzschild well before evaporation. These effects strengthen the Big Bang Nucleosynthesis (BBN) bound on the initial PBH mass by a factor of $\sim 4$--$5$, reduce the mass required for survival to the present epoch to $\sim 2.7\times 10^{14}\,\mathrm{g}$, and shift the viable particle like DM parameter space. Notably the early accretion induced spin-down effect further washes out the well known high-frequency, spin-induced feature in the high frequency stochastic gravitational-wave background, modifying predictions for future detectors.

Figures (14)

• Figure 1: The effective potential $\Phi^{\text{eff}}(r, \theta)$ as a function of the dimensionless radial distance $r/GM$ is plotted. Left Panel: The potential in the equatorial plane ($\theta = \pi/2$) for various spin parameters $a_*$, as indicated by the color bar. Right Panel: The potential at a fixed, high spin ($a_* = 0.99$) for different polar angles $\theta$, from the equator ($\theta = \pi/2$) to the pole.
• Figure 2: Left Panel: Plot of the critical point $y_c \equiv (a x / GM)_c$ as a function of the spin parameter $a_*$ for different polar angles $\theta$, indicated by the color bar, with the equation of state $\omega = 1/3$. Right Panel: Same as the left panel, but for the equatorial plane ($\theta = \pi/2$) and various values of the equation of state $\omega$, shown by the color bar. The black dashed line corresponds to the location of horizon $r_+$.
• Figure 3: Left Panel: Plot of the accretion efficiency parameter $\lambda_{\rm Kerr}(a_*)$ (Eq. \ref{['eq:lambda_kerr']}) as a function of the Kerr spin parameter $a_*$ for different values of the equation of state $\omega$, indicated by the color bar. Right Panel: Variation of $\lambda_{\rm Kerr}(a_*)$ with the spin parameter $a_*$ for the equation of state $\omega = 1/3$. The red dots represent the numerical data, while the blue curve shows the best-fit result given by Eq. \ref{['eq:lambda_fit']}.
• Figure 4: Left Panel: The radial velocity $v(r)$ as a function of dimensionless radius $r/GM$ for a fixed spin parameter $a_* = 0.01$ and equation of state $\omega = 1/3$. The color bar visualizes the variation in the effective accretion rate parameter, $\lambda / \lambda_{\rm Kerr}$, showing how the subsonic and supersonic branches evolve. The flow becomes critical only when the accretion rate equals the critical value, $\lambda = \lambda_{\rm Kerr}$, where the subsonic and supersonic roots merge at the sonic point, marked by the critical speed $c_s = 1/\sqrt{3}$. Right Panel: The flow velocity $v$ at the critical accretion rate is shown as a function of $r$ for an equation of state $\omega = 1/3$. The colour bar indicates the corresponding values of the spin parameter $a_*$. The black dots mark the associated critical points.
• Figure 5: The time evolution of the fluid's thermal properties is shown for a fixed PBH spin $a_* = 0.01$, calculated by substituting the critical transonic velocity profile into the fluid equations. The progression of time is shown by the color bar, representing the ratio of the instantaneous scale factor to the initial scale factor ($a/a_{\text{in}}$). Left Panel: The energy density profile, $\rho / \rho_{\text{in}}$, normalized by its initial value. The vertical dotted line marks the location of the critical radius ($y_c$). Right Panel: The corresponding fluid temperature profile, $T / T_{\text{in}}$, derived from the density profile using $\rho \propto T^4$. The decreasing temperature with the accretion time reflects the cosmological cooling of the background fluid.