A dynamical symmetry of the spherical dust collapse

TL;DR

This paper identifies a scaling symmetry in spherical dust collapse, showing how initial data transformations preserve the collapse outcome and key physical quantities, revealing a fundamental relationship between mass, energy, and size.

Contribution

The paper introduces a novel linear scaling symmetry in dust collapse dynamics that links initial data sets with identical evolution and end states.

Findings

Initial density and shear are invariant under the transformation

The symmetry preserves the collapse outcome and evolution

A scaling relationship between mass, energy, and radius is established

Abstract

By linearly scaling the initial data set (mass and kinetic energy functions) together with the initial area radius of a collapsing dust sphere, we find a symmetry of the collapse dynamics. That is, the linear transformation defines an equivalence class of data sets which lead to the same end result as well as its evolution all through. In particular, the density and shear remain invariant initially as well as during the collapse. What the transformation is exhibiting is an interesting scaling relationship between mass, kinetic energy and the size of the collapsing dust sphere.