Effect of Inhomogeneity on Primordial Black Hole Formation in the Matter
  Dominated Era
  We investigate the effect of inhomogeneity on primordial black hole formation
in the matter dominated era. In the gravitational collapse of an inhomogeneous
density distribution, a black hole forms if apparent horizon prevents
information of the central region of the configuration from leaking. Since
information cannot propagate faster than the speed of light, we identify the
threshold of the black hole formation by considering the finite speed for
propagation of information. We show that the production probability
$\beta_{inhom}(\sigma)$ of primordial black holes, where $\sigma$ is density
fluctuation at horizon entry, is significantly enhanced from that derived in
previous work in which the speed of propagation was effectively regarded as
infinite. For $\sigma \ll 1$, we obtain $\beta_{inhom}\simeq 3.70
\sigma^{3/2}$, which is larger by about an order of magnitude than the
probability derived in earlier work by assuming instantaneous propagation of
information.
