Spherical and nonspherical models of primordial black hole formation:
  exact solutions
  We construct spacetimes which provide spherical and nonspherical models of
black hole formation in the flat Friedmann--Lemaitre--Robertson--Walker (FLRW)
universe with the Lemaitre--Tolman--Bondi solution and the Szekeres
quasispherical solution, respectively. These dust solutions may contain both
shell-crossing and shell-focusing naked singularities. These singularities can
be physically regarded as the breakdown of dust description, where strong
pressure gradient force plays a role. We adopt the simultaneous big bang
condition to extract a growing mode of adiabatic perturbation in the flat FLRW
universe. If the density perturbation has a sufficiently homogeneous central
region and a sufficiently sharp transition to the background FLRW universe, its
central shell-focusing singularity is globally covered. If the density
concentration is sufficiently large, no shell-crossing singularity appears and
a black hole is formed. If the density concentration is not sufficiently large,
a shell-crossing singularity appears. In this case, a large dipole moment
significantly advances shell-crossing singularities and they tend to appear
before the black hole formation. In contrast, a shell-crossing singularity
unavoidably appears in the spherical and nonspherical evolution of cosmological
voids. The present analysis is general and applicable to cosmological nonlinear
structure formation described by these dust solutions.
