Temporal evolution of a radiating star via Lie symmetries

TL;DR

This paper derives the general solution to the temporal evolution equation for a radiating star's collapse using Lie symmetries, revealing new insights into the star's end-state differing from previous models.

Contribution

It provides the first general solution to the temporal evolution equation in radiating star models using symmetry methods, extending beyond previously known particular solutions.

Findings

The general solution alters the predicted end-state of stellar collapse.

It demonstrates the effectiveness of symmetry methods in solving astrophysical evolution equations.

The new solutions suggest different physical behaviors during collapse compared to linear models.

Abstract

In this work, we present for the first time the general solution of the temporal evolution equation arising from the matching of a conformally flat interior to the Vaidya solution. This problem was first articulated by Banerjee et al. (A. Banerjee, S. B. Dutta Choudhury, and Bidyut K. Bhui, Phys. Rev. D, 40 (670) 1989) in which they provided a particular solution to the temporal equation. This simple exact solution has been widely utilized in modeling dissipative collapse with the most notable result being a prediction of the avoidance of the horizon as the collapse proceeds. We study the dynamics of dissipative collapse arising from the general solution obtained via the method of symmetries and of the singularity analysis. We show that the end-state of collapse for our model is significantly different from the widely used linear solution.