On the Polynomial Degeneracy of Ricci Invariants and Spacetime Singularity

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.