  We consider the possibility that the Milky Way's 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.
