We consider the possibility that the Milky Ways dark matter halo possesses a non vanishing equation of state. Consequently, we evaluate the contribution due to the speed of sound, assuming that the dark matter content of the galaxy behaves like a fluid with pressure. In particular, we model the dark matter distribution via an exponential sphere profile in the galactic core, and inner parts of the galaxy whereas we compare the exponential sphere with three widely-used profiles for the halo, i.e. the Einasto, Burkert and Isothermal profile. For the galactic core we also compare the effects due to a dark matter distribution without black hole with the case of a supermassive black hole in vacuum and show that present observations are unable to distinguish them. Finally we investigate the expected experimental signature provided by gravitational lensing due to the presence of dark matter in the core.
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