Genericity aspects of black hole formation in the collapse of spherically symmetric slightly inhomogeneous perfect fluids

TL;DR

This paper investigates how small radial inhomogeneities in spherically symmetric perfect fluid collapse models affect the formation of black holes versus naked singularities, emphasizing the genericity and stability of these outcomes.

Contribution

It introduces a general class of inhomogeneous collapse models with separable mass profiles, demonstrating that naked singularities can generically form from slight inhomogeneities.

Findings

Small inhomogeneities can change black hole outcomes to naked singularities.

The class of models with separable mass profiles naturally leads to naked singularities.

Naked singularities are shown to be a generic outcome in these collapse scenarios.

Abstract

We study the complete gravitational collapse of a class of spherically symmetric inhomogeneous perfect fluid models obtained by introducing small radial perturbations in an otherwise homogeneous matter cloud. Our aim here is to study the genericity and stability of the formation of black holes and locally naked singularities in collapse. While the occurrence of naked singularities is known for many models of collapse, the key issue now in focus is genericity and stability of these outcomes. Towards this purpose, we study how the introduction of a somewhat general class of small inhomogeneities in homogeneous collapse leading to a black hole can change the final outcome to a naked singularity. The key feature that we assume for the perturbation profile is that of a mass profile that is separable in radial and temporal coordinates. The known models of dust and homogeneous perfect fluid collapse can be obtained from this choice of the mass profile as special cases. This choice is very general and physically well motivated and we show that this class of collapse models leads to the formation of a naked singularity as the final state.