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There are two observations of galaxies that can offer some insight into thenature of the dark matter (DM), namely the rotation curves and thegravitational lensing. While the first one can be studied using the Newtonianlimit, the second one is completely relativistic. Each one separately can notdetermine the nature of DM, but both together give us key information aboutthis open problem. In this work we use a static and spherically symmetricmetric to model the DM halo in a galaxy or in a galaxy cluster. The metriccontains two free functions, one associated with the distribution of mass andthe other one with the gravitational potential. We use galactic, typicalrotation curves to univocally determine the kinematics of the halos. We computeseparately the mass functions for a perfect fluid and a scalar field, anddemonstrate that both models can be fitted to the observations, though withdifferent masses. We then employ lensing to discriminate between these models.This procedure represents a test of models using two measurements: rotationcurves and lensing.

Testing DM halos using rotation curves and lensing: A warning on the determination of the halo mass