Galactic rotation curves in brane world models
  In the braneworld scenario the four dimensional effective Einstein equation
has extra source terms, which arise from the embedding of the 3-brane in the
bulk. These non-local effects, generated by the free gravitational field of the
bulk, may provide an explanation for the dynamics of the neutral hydrogen
clouds at large distances from the galactic center, which is usually explained
by postulating the existence of the dark matter. In the present paper we
consider the asymptotic behavior of the galactic rotation curves in the brane
world models, and we compare the theoretical results with observations of both
High Surface Brightness and Low Surface Brightness galaxies. For the chosen
sample of galaxies we determine first the baryonic parameters by fitting the
photometric data to the adopted galaxy model; then we test the hypothesis of
the Weyl fluid acting as dark matter on the chosen sample of spiral galaxies by
fitting the tangential velocity equation of the combined baryonic-Weyl model to
the rotation curves. We give an analytical expression for the rotational
velocity of a test particle on a stable circular orbit in the exterior region
to a galaxy, with Weyl fluid contributions included. The model parameter ranges
for which the $\chi^2$ test provides agreement (within 1$\sigma$ confidence
level) with observations on the velocity fields of the chosen galaxy sample are
then determined. There is a good agreement between the theoretical predictions
and observations, showing that extra-dimensional models can be effectively used
as a viable alternative to the standard dark matter paradigm.
