Formation of primordial black holes

The gravitational collapse of inhomogeneities in the early universe is computed utilizing the hydrodynamic characteristics of Einstein's field equations. It is shown that not only horizon-scale regions of overdensity approximately equal to 1 but also those with this parameter considerably less than 1, collapse to black holes whose mass is greater than or of the order of the horizon mass. The largest black holes are formed when the mass of the inhomogeneous region is greater than that of the corresponding K = 0 Friedmann region. For initial times of 0.001 s onward, a radiation-dominated equation of state is valid throughout all stages of collapse, and the calculations are consequently relevant to the formation of primordial black holes with an approximate range in masses of from 100 to 6,000,000 solar masses. The formation of black holes larger than 6,000,000 solar masses is ruled out by constraints derived from light-element synthesis.