Naked singularities and admissibility of initial conditions

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.