Asymptotic behavior of dynamical variables and naked singularity formation in spherically symmetric gravitational collapse

TL;DR

This paper investigates the conditions leading to naked singularity formation during spherically symmetric gravitational collapse by analyzing the asymptotic behavior of dynamical variables using a novel orthonormal frame formalism.

Contribution

It introduces a new autonomous system of equations for scale-invariant variables in gravitational collapse, providing insights into the asymptotic evolution towards naked singularities.

Findings

Steep spatial density gradients are characteristic of naked singularity formation.

The formalism allows for a detailed analysis of collapse dynamics near singularities.

A conjecture relates density gradients to naked singularity development.

Abstract

Considering gravitational collapse of matter, it is important problem to clarify what kind of conditions leads to the formation of naked singularity. For this purpose, we apply the 1+3 orthonormal frame formalism introduced by Uggla \textit{et al.} to spherically symmetric gravitational collapse of perfect fluid. This formalism allows us to construct an autonomous system of evolution and constraint equations for scale-invariant dynamical variables normalized by the volume expansion rate of the timelike orthonormal frame vector. We investigate the asymptotic evolution of such dynamical variables towards the formation of a central singularity and present a conjecture that the steep spatial gradient for the normalized density function is a characteristic of the naked singularity formation.