  Primordial black holes are analytically and numerically discussed based on
the extended McVittie spacetime solution. By assuming that dark matter and
radiation are the only sources of energy accreted by the forming central
object, it is found that the black-hole mass evolution depends on the initial
mass of the seed, the time in which the black hole emerges, and also on the
average peculiar velocity of dark matter particles. Constraints on the initial
conditions of the primordial black holes are derived from profiles of the
black-hole accretion mechanism and cosmological environment. A large range of
masses is compatible with our approach. In particular, masses of the order of
$10^{10}M_{\odot}$ today may also be generated from small seeds. An incubation
time for the emerging horizons is observed when the initial masses of the seeds
are close to the particle-horizon mass. It is also argued that the
McVittie-type description is consistent with the Schwarzschild solution as long
as other astrophysical processes near the central object are neglected.
