Primordial black hole formation in the matter-dominated phase of the
  Universe
  We investigate primordial black hole formation in the matter-dominated phase
of the Universe, where nonspherical effects in gravitational collapse play a
crucial role. This is in contrast to the black hole formation in a
radiation-dominated era. We apply the Zel'dovich approximation, Thorne's hoop
conjecture, and Doroshkevich's probability distribution and subsequently derive
the production probability $\beta_{0}$ of primordial black holes. The numerical
result obtained is applicable even if the density fluctuation $\sigma$ at
horizon entry is of the order of unity. For $\sigma\ll 1$, we find a
semi-analytic formula $\beta_{0}\simeq 0.05556 \sigma^{5}$, which is comparable
with the Khlopov-Polnarev formula. We find that the production probability in
the matter-dominated era is much larger than that in the radiation-dominated
era for $\sigma\lesssim 0.05$, while they are comparable with each other for
$\sigma\gtrsim 0.05$. We also discuss how $\sigma$ can be written in terms of
primordial curvature perturbations.
