The gravitational collapse of a dust ball

TL;DR

This paper revises the classic Oppenheimer-Snyder model of dust ball collapse, showing that proper matching conditions prevent black hole formation and lead to infinite density at the surface.

Contribution

It corrects the collapse model by enforcing proper metric matching, demonstrating that collapse halts at the Schwarzschild radius and no black hole forms.

Findings

Collapse stops at the Schwarzschild radius

Particles accumulate at the surface with infinite density

Black hole formation is prevented under corrected conditions

Abstract

It is shown that the description of collapse given by the classic model of Oppenheimer and Snyder fails to satisfy a crucial matching condition at the surface of the ball. After correcting the model so that the interior and exterior metrics match correctly, it is established that the contraction process stops at the Schwarzschild radius, that there is an accumulation of particles at the surface of the ball, and that in the limit of infinite time lapse the density of particles at the surface becomes infinite. A black hole cannot form. This result confirms the judgements of both Einstein and Eddington about gravitational collapse when the collapse velocity approaches that of light.