  In this article we find a four-dimensional metric for a large black hole
immersed in dark matter. Specifically, we look for and find a static
spherically symmetric black hole solution to the Einstein equations which
gives, in the Newtonian limit, the rotation curves of galaxies, including the
flat region and the Baryonic Tully-Fisher relation, and which has a regular
horizon. We obtain as well the energy-momentum tensor of the dark matter
sourcing this space-time and it turns, in special, to satisfy the four energy
conditions (dominant, weak, null, and strong) everywhere outside the horizon.
This black-hole-dark-matter system represents a successful simplified model for
galaxies, opens a new area for exploring the relativistic regime of dark
matter, and shows that the theory of General Relativity together with dark
matter can account for the rotation curves of galaxies.
