Self-similar growth of primordial black holes. II - General sound speed

The self-similar growth of primordial black holes is considered for a class of equations of state where pressure equals the square of constant sound speed times energy density, and it is concluded that self-similar growth is possible in regions of the universe provided that the region surrounding the black hole is sufficiently bound. The critical binding energy as a function of the square of sound speed leads to the conclusion that in an initially cold chaotic cosmology, such as considered by Barrow (1977), some black holes could grow to 1000 to 10,000 solar masses. Non-self-similar growth is also briefly considered, and a model is presented for a gravitating pressureless fluid in which the accretion, although it is not self-similar, is nevertheless significant. This suggests that the assertion that a black hole either grows self-similarly or not at all needs to be checked by a complete hydrodynamic computation.