A Note on Singularity Avoidance in Fourth-Order Gravity

Luca Fabbri

doi:10.3390/universe8010051

Abstract

We consider the fourth-order differential theory of gravitation to treat the problem of singularity avoidance: studying the short-distance behaviour in the case of black-holes and the big-bang we are going to see a way to attack the issue from a general perspective.

Highlights

With the detection of gravitational waves, each original experimental prediction of Einstein gravity has been settled
From a purely theoretical perspective, there are yet two problems that need fixing, and which are, more or less, connected: one is solving the nature of singularity formation, which seems to be an occurrence that is unavoidable, in light of the HawkingPenrose theorem; the other, to have gravity made into a renormalizable theory, to fit, with the standard model of particles, into one single framework
Having worked out a rather general way to treat such a singularity problem in the case of black holes, we will move to study the case of the big bang

Summary

Introduction

With the detection of gravitational waves, each original experimental prediction of Einstein gravity has been settled. The solution is simple: raise to 2 the number of curvatures appearing in the Lagrangian This strategy has led to a variety of extensions of Einstein gravity, of which the f (R) types are just the most famous to have arisen in recent times (for a general overview, we refer the reader to [1,2,3,4,5] and references therein). As a matter of fact, a thorough application of the principle requiring continuity for the torsionless limit of any torsion gravity imposes severe restrictions to the possible forms that the gravitational Lagrangian can have [12] By following this principle the Lagrangian found in [12] is the one that grants at most 2 curvatures and the renormalizable kinetic term for torsion [13,14]. Could we have a way to avoid singularity formation, or at least its inevitability, even for early cosmological scenarios?

Fourth-Order Differential Torsion-Gravity

Isotropic Spaces

Black Holes

Big Bang

General Consideration

Conclusions