Galactic Dark Matter and Bertrand Space-times
  Bertrand space-times (BSTs) are static, spherically symmetric solutions of
Einstein's equations, that admit stable, closed orbits. Starting from the fact
that to a good approximation, stars in the disc or halo regions of typical
galaxies move in such orbits, we propose that, under certain physical
assumptions, the dark matter distribution of some low surface brightness (LSB)
galaxies can seed a particular class of BSTs. In the Newtonian limit, it is
shown that for flat rotation curves, our proposal leads to an analytic
prediction of the NFW dark matter profile. We further show that the dark matter
distribution that seeds the BST, is described by a two-fluid anisotropic model,
and present its analytic solution. A new solution of the Einstein's equations,
with an internal BST and an external Schwarzschild metric, is also constructed.
