Admissibility of initial data in spherical collapse

TL;DR

This paper investigates the initial density distributions in spherical gravitational collapse, establishing conditions for admissibility and addressing misconceptions about coordinate choices, with implications for cosmic censorship.

Contribution

It demonstrates that initial density must be an even function of radius in spherical collapse with a non-zero pressure derivative, clarifies misconceptions about coordinate effects, and discusses implications for naked singularities.

Findings

Density distribution must be even in radius for non-zero pressure derivative.

Recent claims about coordinate effects are incorrect.

Strong curvature naked singularities do not violate cosmic censorship.

Abstract

Gravitational collapse of a spherically symmetric cloud has been extensively studied to investigate the nature of resulting singularity. However, there has been considerable debate about the admissibility of certain initial density distributions. Using the Newtonian limit of the equations governing collapse of a fluid with an equation of state p=p(\rho) it is shown that the density distribution has to be even function of r in a spherically symmetric situation provided dp/d\rho \ne 0, even in comoving coordinates. We show that recent claim by Singh that the discrepancy pointed out earlier is due to their use of comoving coordinates is totally incorrect. It is surprising that he expects the use of comoving coordinates to make any difference in this matter. It is also argued that strong curvature naked singularities in gravitational collapse of spherically symmetric dust do not violate the cosmic censorship hypothesis.