Final fate of the spherically symmetric collapse of a perfect fluid

TL;DR

This study numerically investigates the collapse of a perfect fluid in general relativity, revealing conditions under which a naked singularity can form without assuming self-similarity, especially for specific values of the adiabatic index.

Contribution

It demonstrates the formation of naked singularities in spherically symmetric perfect fluid collapse without relying on self-similar assumptions, using a novel numerical approach with observer time coordinates.

Findings

Naked singularities can form at the center for gamma less than approximately 1.01.

The results align with previous self-similar models regarding the critical gamma value.

The study provides a more general numerical confirmation of naked singularity formation.

Abstract

The final fate of the spherically symmetric collapse of a perfect fluid which follows the $\gamma$-law equation of state and adiabatic condition is investigated. Full general relativistic hydrodynamics is solved numerically using a retarded time coordinate, the so-called observer time coordinate. Thanks to this coordinate, the causal structure of the resultant space-time is automatically constructed. Then, it is found that a globally naked, shell-focusing singularity can occur at the center from relativistically high-density, isentropic and time symmetric initial data if $\gamma \alt 1.01$ within the numerical accuracy. The result is free from the assumption of self-similarity. The upper limit of $\gamma$ with which a naked singularity can occur from generic initial data is consistent with the result of Ori and Piran based on the assumption of self-similarity.