All solutions for geodesic anisotropic spherical collapse with shear and heat radiation

TL;DR

This paper introduces the horizon function in geodesic anisotropic spherical collapse, solves its Riccati equation using generating functions, and recovers and extends previous solutions to better understand collapse dynamics.

Contribution

It provides a comprehensive solution framework for the horizon function in anisotropic collapse, unifying and extending prior models.

Findings

All solutions for the horizon function are explicitly derived.

Previous solutions are recovered as special cases.

The approach offers new insights into collapse behavior.

Abstract

We introduce a physically important object, called the horizon function, in the study of geodesic collapse. It is closely related to the stellar characteristics and satisfies a simple Riccati equation. This equation is integrated and all of its solutions are found in terms of some generating functions. Previous solutions are regained and further investigated.