Cold Collapse and Bounce of an FLRW Cloud

TL;DR

This paper investigates the collapse of cold, spherical clouds in general relativity and Newtonian gravity, demonstrating conditions under which a bounce occurs at high densities, with implications for stellar collapse and neutron star physics.

Contribution

It provides a detailed analysis of the conditions for a bounce during collapse, highlighting the roles of curvature and the matter's ground state in GR.

Findings

GR bounce occurs near the matter's ground state with P = -ρ

Significant differences between GR and Newtonian collapse results due to curvature

Both curvature and ground state are essential for GR bounce occurrence

Abstract

We study the collapse of spherical cold clouds beyond black hole formation to investigate the possibility of a bounce in the in-falling matter when a critical density or pressure is reached. As a first step, we analyse the pressureless collapse in general relativity (GR), where an analytic solution exists, and demonstrate that an equivalent Newtonian solution can be derived. Such equivalence also holds for spherically symmetric perfect fluids with uniform density and non-vanishing pressure. We numerically investigate the Newtonian collapse of such clouds with masses of $5$, $20$, and $1000$ M$_\odot$ obeying a polytropic equation of state (EoS). By choosing EoS parameters inspired by typical neutron star conditions, we observe bounces at and above nuclear saturation density. Assuming approximate uniformity, we explore the equivalent GR behaviour of the matter during the bounce. Our findings are as follows: (i) A GR bounce occurs around the ground state of the matter, characterized by $P = -\rho$. (ii) The GR solution differs significantly from the Newtonian result due to the presence of curvature ($k \neq 0$). (iii) Both the curvature and the ground state are crucial factors in allowing a GR bounce to occur.