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.Fil: Aceña, Andrés Esteban. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mendoza. Instituto Interdisciplinario de Ciencias Básicas. - Universidad Nacional de Cuyo. Instituto Interdisciplinario de Ciencias Básicas; ArgentinaFil: Barranco, Juan. Universidad de Guanajuato; MéxicoFil: Bernal, Argelia. Universidad de Guanajuato; MéxicoFil: López, Ericson. Escuela Politécnica Nacional; EcuadorFil: Llerena, Mario. Universidad de La Serena; Chil
