Riccati equations for bounded radiating systems

TL;DR

This paper analyzes Riccati equations governing bounded radiating systems in general relativity, identifying solution categories, applying Lie symmetry analysis, and relating findings to horizon functions and star models.

Contribution

It introduces a systematic classification of solutions, applies Lie symmetry analysis to find new exact solutions, and clarifies relationships among different models in gravitational physics.

Findings

Four solution categories identified based on gravitational potential restrictions

Lie symmetry analysis reveals new classes of exact solutions

Connections established between horizon functions and star models

Abstract

We systematically analyze the nonlinear partial differential equation that determines the behaviour of a bounded radiating spherical mass in general relativity. Four categories of solution are possible. These are identified in terms of restrictions on the gravitational potentials. One category of solution can be related to the horizon function transformation which was recently introduced. A Lie symmetry analysis of the resulting Riccati equation shows that several new classes of exact solutions are possible. The relationship between the horizon function, Euclidean star models and other earlier investigations is clarified.