On the Rotation Curve of Disk Galaxies in General Relativity

Recently, it has been suggested that the phenomenology of flat rotation curves observed at large radii in equatorial plane disk galaxies can be explained as a manifestation General Relativity instead effect Dark Matter halos. In this paper, by using well known weak field, low velocity gravitomagnetic formulation GR, expected GR are rigorously obtained for purely baryonic models with realistic density profiles, and compared predictions newtonian gravity same disks absence Matter. As expected, resulting indistinguishable, corrections all order $v^2/c^2\approx 10^{-6}$. Next, Jeans equations two-integral stellar systems derived, then solved Miyamoto-Nagai model, showing finite-thickness effects do not change previous conclusions. Therefore, galactic requires exactly gravity, unless cases here explored reconsidered full framework substantially different results (with surprising consequence field approximation cannot applied to study rotating regime). mathematical is described detail, so present extended other models, or elliptical (where also required but their rotational support much less than galaxies).