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

Repulsive gravity near naked singularities and point massive particles