  This work is part of an ongoing research programme to study possible
Primordial Black Hole (PBH) formation during the radiation dominated era of the
early universe. Working within spherical symmetry, we specify an initial
configuration in terms of a curvature profile, which represents initial
conditions for the large amplitude metric perturbations, away from the
homogeneous Friedmann Robertson Walker model, which are required for PBH
formation. Using an asymptotic quasi-homogeneous solution, we relate the
curvature profile with the density and velocity fields, which at an early
enough time, when the length scale of the configuration is much larger than the
cosmological horizon, can be treated as small perturbations of the background
values. We present general analytic solutions for the density and velocity
profiles. These solutions enable us to consider in a self-consistent way the
formation of PBHs in a wide variety of cosmological situations with the
cosmological fluid being treated as an arbitrary mixture of different
components with different equations of state. We show that the analytical
solutions for the density and velocity profiles as functions of the initial
time are pure growing modes. We then use two different parametrisation for the
curvature profile and follow numerically the evolution of a range of initial
configuration.
