Some comments on the nature of initial data in spherical collapse

TL;DR

This paper defends the validity of previous analyses on dust collapse by clarifying coordinate usage and refutes claims about the instability of naked singularities, emphasizing the importance of coordinate choice in gravitational collapse studies.

Contribution

It clarifies the coordinate dependence in dust collapse models and refutes claims about naked singularity instability, reinforcing the validity of earlier results.

Findings

Antia's criticism based on Eulerian coordinates is invalid.

Lagrangian coordinates do not restrict density series to even powers.

Previous claims on naked singularity instability lack concrete support.

Abstract

Various authors have shown the occurence of naked singularities and black holes in the spherical gravitational collapse of inhomogeneous dust. In a recent preprint, Antia has criticised a statement in a paper by Jhingan, Joshi and Singh on dust collapse. We show that his criticism is invalid. Antia shows that in Eulerian coordinates a series expansion for the density of a collapsing Newtonian fluid can have only even powers. However, he has overlooked the fact that Jhingan et al. have actually used Lagrangian (comoving) coordinates, and not Eulerian coordinates. As we show, in Lagrangian coordinates there is no restriction that the density have only even powers and hence his criticism is invalid. We also point out that an earlier claim by Antia on the instability of strong naked singularities in dust collapse is not supported by any concrete analysis, and is hence incorrect.