We demonstrate a very general mathematical and physical expression of the rotation speed at the end of the galaxy (far from the vast majority of the galaxy’s baryonic mass) obtained from General Relativity without non-baryonic matter. We show the excellent agreement with measurements obtained for the Milky Way published in a recent article which confirms a significantly faster decline in the circular velocity curve at outer galactic radii up to 30 kpc compared to the inner parts. This relation comes from Linearized General Relativity (GRL). Some papers argue that the GRL solution cannot explain dark matter (DM). We demonstrate that this conclusion is too premature because they only consider mass currents of the galaxies which is not the most general theoretical solution. And because this GRL explanation suffers from the same defects as exotic matter, only direct measurement of the Lense-Thirring effect can objectively reject this solution. Current experiments are not yet precise enough to test this solution. But meanwhile, if the relevance of this expression were confirmed for most galaxies, this would strongly challenge exotic matter to explain DM and could drastically change the point of view on the DM component. Two known physical fields (contrary to an exotic matter) which are until now neglected or rather underestimated would then explain DM. The DM mystery would then consist for theory in understanding how the values of these fields can be larger than expected and for observation in being able to measure these two fields with sufficient precision. In addition, these fields allow obtaining the TULLY-FISHER relation and the MOND theory.