On the polynomial degeneracy of Ricci invariants and spacetime singularity

We explore the connection of a general relativistic matter-energy momentum tensor with the polynomial degeneracies of 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, $\left(ii\right)$ an isotropic sphere or $\left(iii\right)$ a distribution with negative pressure.