Spherically symmetric perfect fluid in area-radial coordinates

TL;DR

This paper analyzes the collapse of a perfect fluid under spherical symmetry using area-radial coordinates, revealing conditions for static centers and the nature of singularities based on mass functions.

Contribution

It introduces a framework for describing perfect fluid collapse in area-radial coordinates and links mass functions to singularity formation.

Findings

Analytic mass functions describe static regular centers.

Central singularities require infinite density discontinuities.

Fluid dynamics at the center influence singularity characteristics.

Abstract

We study the spherically symmetric collapse of a perfect fluid using area-radial coordinates. We show that analytic mass functions describe a static regular centre in these coordinates. In this case, a central singularity can not be realized without an infinite discontinuity in the central density. We construct mass functions involving fluid dynamics at the centre and investigate the relationship between those and the nature of the singularities.