Testing DM halos using rotation curves and lensing: A warning on the
  determination of the halo mass
  There are two observations of galaxies that can offer some insight into the
nature of the dark matter (DM), namely the rotation curves and the
gravitational lensing. While the first one can be studied using the Newtonian
limit, the second one is completely relativistic. Each one separately can not
determine the nature of DM, but both together give us key information about
this open problem. In this work we use a static and spherically symmetric
metric to model the DM halo in a galaxy or in a galaxy cluster. The metric
contains two free functions, one associated with the distribution of mass and
the other one with the gravitational potential. We use galactic, typical
rotation curves to univocally determine the kinematics of the halos. We compute
separately the mass functions for a perfect fluid and a scalar field, and
demonstrate that both models can be fitted to the observations, though with
different masses. We then employ lensing to discriminate between these models.
This procedure represents a test of models using two measurements: rotation
curves and lensing.
