A Riccati equation in radiative stellar collapse

TL;DR

This paper derives and solves a Riccati equation governing relativistic gravitational collapse with heat flux, providing new closed-form solutions that generalize previous models and explore temperature behavior in inhomogeneous spacetimes.

Contribution

It introduces two classes of new solutions to the Riccati equation in gravitational collapse, extending previous models with more general spatial dependence.

Findings

New closed-form solutions for gravitational collapse models

General spatial dependence in metric functions

Insights into temperature behavior in inhomogeneous spacetimes

Abstract

We model the behaviour of a relativistic spherically symmetric shearing fluid undergoing gravitational collapse with heat flux. It is demonstrated that the governing equation for the gravitational behaviour is a Riccati equation. We show that the Riccati equation admits two classes of new solutions in closed form. We regain particular models, obtained in previous investigations, as special cases. A significant feature of our solutions is the general spatial dependence in the metric functions which allows for a wider study of the physical features of the model, such as the behaviour of the causal temperature in inhomogeneous spacetimes.