  A massive star undergoes a continual gravitational collapse when the
pressures inside the collapsing star become insufficient to balance the pull of
gravity. The Physics of gravitational collapse of stars is well studied. Using
general relativistic techniques one can show that the final fate of such a
catastrophic collapse can be a black hole or a naked singularity, depending
upon the initial conditions of gravitational collapse. While stars are made of
baryonic matter whose collapse is well studied, there is good indirect evidence
that another type of matter, known as dark matter, plays an important role in
the formation of large-scale structures in the universe, such as galaxies. It
is estimated that some eighty-five percent of the total matter in the universe
is dark matter. Since the particle constituent of dark matter is not known yet,
the gravitational collapse of dark matter is less explored. Here we consider
first some basic properties of baryonic matter and dark matter collapse. Then
we discuss the final fate of gravitational collapse for different types of
matter fields and the nature of the singularity which can be formed as an
endstate of gravitational collapse. We then present a general relativistic
technique to form equilibrium configurations and argue that this can be thought
of as a general relativistic analog of the standard virialization process. We
suggest a modification, where the Top-Hat collapse model of primordial dark
matter halo formation is modified by using the general relativistic technique
of equilibrium. We also explain why this type of collapse process is more
likely to happen in dark matter fields.
