On the Polynomial Degeneracy of Ricci Invariants and Spacetime Singularity

TL;DR

This paper investigates how polynomial degeneracies of higher order curvature invariants relate to the energy-momentum tensor in general relativity, revealing conditions under which spacetime singularities may be avoided during gravitational collapse.

Contribution

It establishes a link between curvature invariant degeneracies and constraints on matter-energy tensors, identifying specific conditions that prevent singularity formation.

Findings

Singularity formation is possible only with dust, isotropic spheres, or negative pressure distributions.

Polynomial degeneracies impose additional constraints on the energy-momentum tensor.

Not all gravitational collapses necessarily lead to singularities under these conditions.

Abstract

We explore the connection of a general relativistic matter-energy momentum tensor with the polynomial degeneracies of higher order curvature invariants defined in Riemannian geometry. The degeneracies enforce additional constraints on the energy-momentum tensor components. Due to these constraints the formation of a curvature singularity, for instance during a gravitational collapse can no longer be treated as inevitable. We find that there can be a formation of singularity iff the interior fluid evolves into (i) a pressure-less dust, (ii) an isotropic sphere or (iii) a distribution with negative pressure.