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 asymptotically 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.

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