Self-gravitating fluid systems and galactic dark matter
  We study gravitational collapse with anisotropic pressures, whose end stage
can mimic space-times that are seeded by galactic dark matter. To this end, we
identify a class of space-times (with conical defects) that can arise out of
such a collapse process, and admit stable circular orbits at all radial
distances. These have a naked singularity at the origin. An example of such a
space-time is seen to be the Bertrand space-time discovered by Perlick, that
admits closed, stable orbits at all radii. Using relativistic two- fluid
models, we show that our galactic space-times might indicate exotic matter, i.e
one of the component fluids may have negative pressure for a certain asymptotic
fall off of the associated mass density, in the Newtonian limit. We complement
this analysis by studying some simple examples of Newtonian two-fluid systems,
and compare this with the Newtonian limit of the relativistic systems
considered.
