Final fate of the spherically symmetric collapse of a perfect fluid

Abstract

The final fate of the spherically symmetric collapse of a perfect fluid which follows the $γ$-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 $γ\alt 1.01$ within the numerical accuracy. The result is free from the assumption of self-similarity. The upper limit of $γ$ 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.