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 \sim 10 ^ { -4 } s to t \sim 10 ^ { 2 } s after the Big Bang .
Our results indicate that small PBHs with initial masses between 10 ^ { -4 } to 1 M _ { \odot } may grow up to hundreds of solar masses , and thus can be SMBH seeds .
On the other hand , PBHs formed at t \sim 1 s with initial mass between 900 and \sim 980 M _ { \odot } , by the time t \sim 100 s show masses of 10 ^ { 4 } to 10 ^ { 6 } M _ { \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 .