Repulsive gravity near naked singularities and point massive particles

We investigate the existence of repulsive gravitational acceleration near naked singularities. The investigation is carried out by means of the acceleration tensor, which is a coordinate invariant object. We find that the gravitational acceleration is repulsive in the vicinity of the origin in the Reissner-Nordstr{\o}m and in the Kerr space-times, and attractive at large distances in the expected Newtonian way. We further address the space-time of a point massive particle, which also exhibits repulsive effects near the origin.