The Exact Solutions to the Gravitational Contraction in Comoving Coordinate System

TL;DR

This paper investigates gravitational collapse in comoving coordinates, deriving exact solutions for dust collapse, identifying solution types, and discovering a new singularity whose origin remains unclear.

Contribution

It provides exact solutions for dust gravitational collapse in comoving coordinates and analyzes the nature of these solutions and singularities.

Findings

Comoving coordinates are compatible only with zero-pressure free-falling particles.

Three types of solutions for dust collapse: oscillating, critical, and open trajectories.

A new kind of singularity was identified, with an unclear origin.

Abstract

The gravitational collapse of a star is a warmly discussed but still puzzling problem, which not only involves the dynamics of the gases, but also the subtle coordinate transformation. In this letter, we give some more detailed investigation on this problem, and reach the results: (I). The comoving coordinate system for the stellar system is only compatible with the zero-pressure free falling particles. (II). For the free falling dust, there are three kind of solutions respectively corresponding to the oscillating, the critical and the open trajectories. The solution of Oppenheimer and Snyder is the critical case. (III). All solutions are exactly derived. There is a new kind singularity in the solution, but its origin is unclear.