The general relativistic geometry of the Navarro-Frenk-White model

We derive the space time geometry associated with the Navarro Frenk White dark matter galactic halo model. We discuss several properties of such a spacetime, with particular attention to the corresponding Newtonian limit, stressing the qualitative and quantitative nature of the differences between the relativistic and the Newtonian description. We also discuss on the characteristics of the possible stress energy tensors which could produce such a geometry, via the Einstein's equations.