The Structure of Singularity in Gravitational Collapse

TL;DR

This paper investigates the formation of singularities, including black holes and naked singularities, in spherically symmetric gravitational collapse of dust and perfect fluids, establishing conditions under which these phenomena occur from generic initial data.

Contribution

It demonstrates that strong naked singularities can form from generic initial density profiles and extends analysis to perfect fluids with equation of state p=kρ.

Findings

Strong naked singularities arise for generic density profiles.

Black hole formation also occurs under similar conditions.

Results hold for perfect fluids with p=kρ and weak energy condition.

Abstract

We will describe here the structure of singularity forming in gravitational collapse of spherically symmetric inhomogeneous dust. Such a collapse is described by the Tolman-Bondi-Lema{\^i}tre metric. The main new result here relates, in a general way, the formation of black holes and naked shell-focusing singularities resulting as the final fate of such a collapse to the generic form of regular initial data. Such a data is characterized in terms of the density and velocity profiles of the matter, specified on an initial time slice from which the collapse commences. We show that given any generic density profile at the initial time slice, there exists a corresponding velocity profile which gives rise to a strong curvature naked singularity. This establishes that strong naked singularities arise for a generic density profile. We also establish here that similar results hold for black hole formation as well. Keeping the model to be spherically symmetric we also consider more general form of matter fields, i.e. equation of state $p = k\rho$. We will analyse here the nature of non-central singularity forming due to collapse of spherically symmetric perfect fluid subject to weak energy condition.