  In an arbitrary axisymmetric stationary spacetime, we determine the
expression for the tangential velocity of test objects following a circular
stable geodesic motion in the equatorial plane, as function of the metric
coefficients. Next, we impose the condition, observed in large samples of disks
galaxies, that the magnitude of such tangential velocity be radii independent,
obtaining a constraint equation among the metric coefficients, and thus
arriving to an iff condition: The tangential velocity of test particles is
radii independent iff the metric coefficients satisfied the mentioned
constraint equation. Furthermore, for the static case, the constraint equation
can be easily integrated, leaving the spacetime at the equatorial plane
essentially with only one independent metric coefficient. With the geometry
thus fixed, we compute the Einstein tensor and equate it to and arbitrary
stress energy tensor, in order to determined the type of energy-matter which
could produce such a geometry. Within an approximation, we deduce a constraint
equation among the components of the stress energy tensor. We test in that
constraint equation several well known types of matter, which have been
proposed as dark matter candidates and are able to point for possible right
ones. Finally, we also present the spherically symmetric static case and apply
the mentioned procedure to perfect fluid stress energy tensor, recovering the
Newtonian result as well as the one obtained in the axisymmetric case. We also
present arguments on the need to use GR to study non dust types of matter.
