We analyze the intriguing possibility of explaining both dark mass components in a galaxy: the dark matter (DM) halo and the supermassive dark compact object lying at the center, by a unified approach in terms of a quasi-relaxed system of massive, neutral fermions in general relativity. The solutions to the mass distribution of such a model that fulfill realistic halo boundary conditions inferred from observations, develop a high-density core supported by the fermion degeneracy pressure able to mimic massive black holes at the center of galaxies. Remarkably, these dense core-diluted halo configurations can explain the dynamics of the closest stars around Milky Way’s center (SgrA*) all the way to the halo rotation curve, without spoiling the baryonic bulge-disk components, for a narrow particle mass range $m c^{2} \sim 10$ – $1 0^{2}$ keV.

This essay is awarded third prize in the 2019 Essay Competition of the Gravity Research Foundation.

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