Evolution of primordial black holes

There has been recent interest in the possibility of the existence of black holes with mass far smaller than the solar mass. At the present time, the only plausible mechanism that may lead to the production of such small black holes seems to be through the formation of overdense regions at a very short time after the creation of the universe. One would expect such overdensities to arise from statistical fluctuations. This work attempts to set up a formalism that can be used to determine the way inhomogeneities could lead to collapse and formation of black holes. The evolution of spherically symmetric inhomogeneities arising in a background Friedmann space is analyzed. The method of solution is to set up a perturbation series strongly convergent for small density fluctuations. The differential equation governing the perturbation of any given order is determined. The first-order solutions are found, and they are used to describe the evolution of the perturbed space starting from a given initial localized overdensity. The criteria for collapse ae obtained in the model, and these criteria are used to determine the number of primordial black holes one could possibley observe today