A Riccati equation in radiative stellar collapse
arXiv:0808.2101 · doi:10.1063/1.2832628
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.
13 pages, To appear in J. Math. Phys