Analysis of instability of systems composed by dark and baryonic matter
  In this work the dynamics of self-gravitating systems composed by dark and
baryonic matter is analyzed. Searching for a description of this dynamics, a
system of collisionless Boltzmann equations for the two constituents and the
Poisson equation for the gravitational field are employed. Through the solution
of these equations the collapse criterion is determined from a dispersion
relation. The collapse occurs in an unstable region where the solutions grow
exponentially with time. It is shown that the unstable region becomes larger if
the dispersion velocity of dark matter becomes larger than the one of the
baryonic matter. The results obtained are also compared with the case where
only the dark matter is present. The model of the present work has a higher
limit of instability and therefore, exhibited an advantage in the structure
formation.
