Singular Isotropic Cosmologies and Bel-Robinson Energy

TL;DR

This paper classifies possible spacetime singularities in isotropic FRW universes using Bel-Robinson energy, providing a comprehensive framework to distinguish and analyze different singularity types in general relativity.

Contribution

It introduces a novel approach using Bel-Robinson energy to classify and analyze singularities in isotropic cosmologies, extending understanding of their generic behaviors across geometries.

Findings

Complete classification of singularities in isotropic universes.

Demonstration that known singular behaviors are generic across spatial geometries.

Use of Bel-Robinson energy as a key tool for singularity analysis.

Abstract

We consider the problem of the nature and possible types of spacetime singularities that can form during the evolution of \emph{FRW} universes in general relativity. We show that by using, in addition to the Hubble expansion rate and the scale factor, the Bel-Robinson energy of these universes we can consistently distinguish between the possible different types of singularities and arrive at a complete classification of the singularities that can occur in the isotropic case. We also use the Bel-Robinson energy to prove that known behaviours of exact flat isotropic universes with given singularities are generic in the sense that they hold true in every type of spatial geometry.