Naked singularities and admissibility of initial conditions

TL;DR

This paper investigates the conditions under which naked singularities can form during gravitational collapse, showing that initial density distributions must be symmetric and exploring implications for naked singularity formation.

Contribution

It demonstrates that initial density profiles must be even functions of radius in spherical collapse with non-zero pressure derivatives, impacting naked singularity formation theories.

Findings

Density distribution must be an even function of radius

Implications for the formation of strong naked singularities

Constraints on initial conditions for gravitational collapse

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 $dp/d\rho\ne0$. Implications of this result on formation of strong naked singularities are examined.