The evolution of primordial black hole masses in the radiation- dominated era

We revisit the problem of PBH mass evolution in the radiation-dominated era. We solve the complete differential equation in the semiclassical regime with absorption and evaporation terms and show that PBHs can gain very little mass, if at all, in this era. Relativistic proper motion of PBHs respect to the CMBR, as a possible loophole in the growth argument, is shown to be unlikely. Finally we demonstrate that PBHs can not remain in thermodynamical equilibrium with the ambient radiation, and therefore initially non-evaporating black holes must enter the evaporating regime, supporting several efforts to look for observational signatures.