Galactic dark matter effects from purely geometrical aspects of General Relativity

We study disc galaxies in the framework of General Relativity to focus on the possibility that, even in the low energy limit, there are relevant corrections with respect to the purely Newtonian approach. Our analysis encompasses the model both considering a low energy expansion and exact solutions, making it clear the connection between these different approaches. In particular, we focus on two different limits: the well known gravitomagnetic analogy and a new limit, called strong gravitomagnetism, which has corrections in c of the same order as the Newtonian terms. We show that these two limits of the general class of solution can account for the observed flat velocity profile, contrary to what happens using Newtonian models, where a dark matter contribution is required. Hence, we suggest a geometrical origin for a certain amount of dark matter effects.