TULLY-FISHER Law Demonstrated by General Relativity and Dark Matter

The Tully-Fisher law M ∝ v^α is an empirical relationship between the mass of a galaxy and its asymptotic rotation velocity. The purpose of this research is to demonstrate that this relation can be theoretically obtained in General Relativity (GR) with a particular solution of dark matter (DM) in very good agreement with the observations. Several years ago, it was demonstrated that DM can theoretically be completely explained by a natural effect of GR without exotic matter, the Lense-Thirring effect that exists exclusively in GR. In this explanation, the field generating the Lense-Thirring effect would be generated by the clusters of galaxies and not by the own field of the galaxy which is negligible. In this way, a uniform field (from galaxies’ clusters) would embed the galaxies. We retrieve the coefficients of this law thanks to the explicit values of this field required to explain DM. This demonstration shows how relevant this explanation of the DM is, not only theoretically (by obtaining the expression of the law) but also practically (by obtaining the coefficients from the values required to explain the DM). The Tully-Fisher law would then reveal the Lense-Thirring effect of the clusters of galaxies on the galaxies.