Rotation Curves of Galaxies via Reissner-Nordstrom Induced Gravity and an Alternative Explanation of Dark Matter

The dynamics of a neutral test particle in the spacetime geometry cor-responding to a central massive and charged object (Reissner-Nordstrom Metric) is examined. For a radial distance r = Q^2/M (in natural units) the gravitational force is null, independently of the value of G, and repulsive below this value. It is shown that within typical atomic and molecular distances, there is a repulsive force albeit negligible in comparison with the electromagnetic one ruling the atomic world. For an eventual extremal black hole having a mass equal to the Planck Mass a limit to electric charge equal to 1(MeV )^0 is found. At the galactic scale and for galaxies with a compact central nucleus with mass below or of the order of the Solar mass, the repulsive force can reproduce the flat rotation curve of stellar orbits observed in many galaxies.