Self-similar growth of primordial black holes. I - Stiff equation of state

The possible self-similar growth of primordial black holes in a 'stiff' early Universe is discussed. It is concluded that such growth is possible only if the black hole accretes the matter as a null-fluid inside a certain surface, called here the phase-change surface. This has made it necessary to match an ingoing self-similar Vaidya solution to the self-similar p = epsilon matter solution. The rarefaction waves that play an essential role in the accretion flow are also discussed. Numerically, agreement is obtained with an earlier result by Lin et al., that the maximum mass reached by primordial black holes in the stiff era is about 1 solar mass. However, the present description of the process is quite different. Moreover, it is felt that whether there is rapid growth of black holes in softer epochs of the Universe is as yet undecided, pending a proper discussion of the weak discontinuities (critical points) in the self-similar flow.