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Perfect Fluid Dark Matter
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Taking the flat rotation curve as input and treating the matter content in the galactic halo region as perfect fluid, we obtain space time metric at the galactic halo region in the framework of general relativity. We find that the resultant metric is a non-relativistic-dark-matter-induced space-time embedded in a static Friedmann-Lema\^itre-Robertson-Walker universe. This means that the flat rotation curve not only leads to the existence of dark matter but also suggests the background geometry of the universe. The flat rotation curve and the demand that the dark matter be non-exotic together indicate a (nearly) flat universe as favored by the modern cosmological observations. We obtain the expressions for energy density and pressure of dark matter halo and consequently the equation of state of dark matter. Various other aspects of the solution are also analyzed.
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Horizon-scale tests of gravity theories and fundamental physics from the Event Horizon Telescope image of Sagittarius A$^*$
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