The spacetime associated with galactic dark matter halos

We show how an adequate post-Newtonian generalization can be obtained for Newtonian dark matter halos associated with an empiric density profile. Applying this approach to halos that follow from the well known numerical simulations of Navarro, Frenk and White (NFW), we derive all dynamical variables and show that NFW halos approximately follow an ideal gas type of equation of state which fits very well to a polytropic relation in the region outside the core. This fact suggests that outer regions of NFW halos might be related to equilibrium states in the non-extensive Statistical Mechanics formalism proposed by Tsallis.