Rotation curves of disk galaxies and General Relativity

Abstract: It has been proposed that the flat rotation curves observed at large radii in disk galaxies can be interpreted as an effect of General Relativity (GR) instead of the presence of dark matter (DM) halos in Newtonian gravity. In Ciotti (2022) the problem is rigorously explored in the special setting of the weak-field, low-velocity gravitomagnetic limit of GR. The rotation curves are obtained for purely baryonic disk models with realistic density profiles, and compared with the predictions of Newtonian gravity for the same disks, in absence of DM. The rotation curves are indistinguishable, with percentual GR corrections at all radii of the order of $\approx 10^{-6}$ or less, so that DM halos are required in gravitomagnetism as in Newtonian gravity. From a more general point of view, a list of the most urgent problems that must be addressed by any proposed GR-based alternative to the existence of DM, is given.