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 the 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 the 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 << 1, we obtain beta(inhom) similar or equal to 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.