Bianchi IX gravitational collapse of matter inhomogeneities
  We investigate a model of gravitational collapse of matter inhomogeneities
where the latter are modelled as Bianchi type IX (BIX) spacetimes. We found
that this model contains, as limiting cases, both the standard spherical
collapse model and the Zeldovich solution for a 1-dimensional perturbation. We
study how these models are affected by small anisotropic perturbations within
the BIX potential. For the spherical collapse case, we found that the model is
equivalent to a closed FLRW Universe filled with matter and two perfect fluids
representing the anisotropic contributions. From the linear evolution up to the
turnaround, the anisotropies effectively shift the value of the FLRW spatial
curvature, because the fluids have effective Equation of State (EoS) parameters
$w \approx -1/3$. Then we estimate the impact of such anisotropies on the
number density of haloes using the Press-Schechter formalism. If a fluid
description of the anisotropies is still valid after virialization, the
averaged over time EoS parameters are $w\approx 1/3$. Using this and demanding
hydrostatic equilibrium, we find a relation between the mass $M$, the average
radius $R$ and the pressure $p$ of the virialized final structure. When we
consider perturbations of the Zeldovich solution, our qualitative analysis
suggests that the so called \textit{pancakes} exhibit oscillatory behavior, as
would be expected in the case of a vacuum BIX spacetime.
