The role of anisotropy and inhomogeneity in Lemaitre-Tolman-Bondi collapse

TL;DR

This paper investigates how initial shear and density inhomogeneities influence the formation of naked singularities in spherically symmetric dust collapse, revealing that these features alone do not determine the end state.

Contribution

It demonstrates that initial shear and density contrast are not individually sufficient to predict collapse outcomes and introduces invariance properties of these features under certain transformations.

Findings

Same initial shear can lead to different end states.

Initial shear and density contrast are invariant under specific transformations.

The nature of singularities can be determined if both initial shear and density contrast are known.

Abstract

We study the effects of shear and density inhomogeneities in the formation of naked singularities in spherically symmetric dust space--times. We find that in general neither of these physical features alone uniquely specifies the end state of the gravitational collapse. We do this by (i) showing that, for open sets of initial data, the same initial shear (or initial density contrast) can give rise to both naked and covered solutions. In particular this can happen for zero initial shear or zero initial density contrast; (ii) demonstrating that both shear and density contrast are invariant under a one parameter set of linear transformations acting on the initial data set and (iii) showing that asymptotically (near the singularities) one cannot in general establish a direct relationship between the rate of change of shear (or density contrast) and the nature of the singularities. However, one can uniquely determine the nature of the singularity if both the initial shear and initial density contrast are known. These results are important in understanding the effects of the initial physical state and in particular the role of shear, in determiming the end state of the gravitational collapse.