PBH mass growth through radial accretion during the radiation dominated era

We model the radial accretion of radiation on Primordial Black Holes (PBH) by numerically solving Einstein's equations coupled to an ultrarelativistic ideal gas with equation of state $p=\rho/3$. We calculate the final mass of a black hole by the integration of the accreted radiation energy density during the leptonic era between $t\sim10^{-4}s$ to $t\sim 10^2s$ after the Big Bang. Our results indicate that small PBHs with initial masses between $10^{-4}$ to $1M_{\odot}$ may grow up to hundreds of solar masses, and thus can be SMBH seeds. On the other hand, PBHs formed at $t\sim 1s$ with initial mass between 900 and $\sim 980M_{\odot}$, by the time $t\sim 100s$ show masses of $10^4$ to $10^6M_{\odot}$ which are masses of seeds or already formed SMBHs. The fact that we consider only radial flow implies that our results work well as limiting cases, and it is expected that under more general scenarios the accretion rates may change significantly. Nevertheless we show that it is possible that SMBHs can be PBHs that grew due to the accretion of radiation.