Compact objects from gravitational collapse: an analytical toy model

TL;DR

This paper presents an analytical method to model the formation of static compact objects from gravitational collapse, providing a bridge between dynamic collapse processes and stable configurations in general relativity.

Contribution

It introduces a procedure to derive regular static configurations from dynamical collapse models under general physical assumptions.

Findings

A class of perfect fluid collapse models leading to static constant density objects.

The method can potentially describe the formation of real compact objects.

Illustrative models demonstrate the transition from collapse to equilibrium.

Abstract

We develop here a procedure to obtain regular static configurations as resulting from dynamical gravitational collapse of a massive matter cloud in general relativity. Under certain general physical assumptions for the collapsing cloud, we find the class of dynamical models that lead to an equilib- rium configuration. To illustrate this, we provide a class of perfect fluid collapse models that lead to a static constant density object as limit. We suggest that similar models might possibly constitute the basis for the description of formation of compact objects in nature.