A New Result on the Dynamical Symmetry of Spherical Collapse

TL;DR

This paper investigates a dynamical symmetry in spherical collapse, showing that specific initial conditions lead to invariant evolution of physical parameters, while the final outcome depends on initial radius choice.

Contribution

It introduces a new dynamical symmetry in spherical collapse using linear transformations of initial data and initial radius, revealing invariance properties.

Findings

Physical parameters remain invariant under the symmetry transformation.

Final collapse outcome depends on initial area radius.

Proper initial radius choice influences collapse evolution.

Abstract

A dynamical symmetry for spherical collapse has been studied using a linear transformation of the initial data set (mass and kinetic energy function) and the area radius. With proper choice of the initial area radius, the evolution as well as the physical parameters namely energy density and shear remain invariant both initially and at any time instant. Finally, it is found that the final outcome of collapse depends on the initial choice of the area radius.