Singularity avoidance in classical gravity from four-fermion interaction

We derive the dynamics of the gravitational collapse of a homogeneous and spherically symmetric cloud in a classical set-up endowed with a topological sector of gravity and a non-minimal coupling to fermions. The effective theory consists of the Einstein-Hilbert action plus Dirac fermions interacting through a four-fermion vertex. At the classical level we obtain the same picture that has been recently studied by some of us within a wide range of effective theories inspired by a super-renormalizable and a symptotically free theory of gravity. The classical singularity is replaced by a bounce beyond which the cloud re-expands indefinitely. We thus show that even at a classical level if we allow for a non-minimal coupling of gravity to fermions event horizons may never form for a suitable choice of some parameters of the theory. (C) 2014 The Authors. Published by Elsevier B.V