2018MNRAS.475.2204C

The observed motion of stars close to galaxy nuclei shows that the resulting velocities are small of the order of a few hundred of km s^–1. In these regions of strong gravity, the Newtonian gravitational field or even a post-Newtonian approximation may not be adequate to describe the motion of stars. In this paper, we study the possibility that the rotation curves problem may be explained mostly in the realm of Einstein's general relativity in a nearly weak field regime. By using the geodesic equations to obtain a gravitational potential generated from a point-like source, we end up in the concept of a nearly Newtonian gravity, and we show that its resulting potential responds to the dark halo mostly attributed to dark matter. We show that it comes essentially from the propagation of the non-linear effects of the obtained effective velocity field. As a test, we study a sample of 27 low surface brightness galaxies (LSBGs) and nine dwarf galaxies obtaining rotation curve shapes in nearly agreement with observations.