  Spherically symmetric and static dark matter halos in hydrostatic equilibrium
demand that dark matter should have an effective pressure that compensates the
gravitational force of the mass of the halo. An effective equation of state can
be obtained for each rotational velocity profile of the stars in galaxies. In
this work, we study one of this dark matter equation of state obtained for the
Universal Velocity Profile and analyze the properties of the self-gravitating
structures that emerges from this equation of state. The resulting
configurations explaining the observed rotational speeds are found to be
unstable. We conclude that either the halo is not in hydrostatic equilibrium,
or it is non spherically symmetric, or it is not static if the Universal
Velocity profile should be valid to fit the rotational velocity curve of the
galaxies.
