Geodesic completeness of singularity free gravity

Abstract

Generalizing the gravitational potential first proposed in [1] we derive a large class of relativistic singularity free theories of gravity, which reduce to flat spacetime at large distances. We verify that for the chosen gravitational potential the force and the space-time curvature resolve the singularity and vanish at large distances. We show that those singularity free black hole solutions generically have a two horizon structure. Furthermore, we show that there is a subclass of potentials which produce a geometries geodesically complete through the origin. We discuss the implications of the effects resulting from such theories and show that black holes solutions are predicted to have minimum allowed mass.