A Riccati equation in radiative stellar collapse
Abstract
We model the behavior of a relativistic spherically symmetric shearing fluid undergoing gravitational collapse with heat flux. It is demonstrated that the governing equation for the gravitational behavior 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 behavior of the causal temperature in inhomogeneous spacetimes.
 Publication:

Journal of Mathematical Physics
 Pub Date:
 January 2008
 DOI:
 10.1063/1.2832628
 arXiv:
 arXiv:0808.2101
 Bibcode:
 2008JMP....49a2501R
 Keywords:

 95.30.Sf;
 97.60.s;
 95.30.Lz;
 04.20.q;
 Relativity and gravitation;
 Late stages of stellar evolution;
 Hydrodynamics;
 Classical general relativity;
 General Relativity and Quantum Cosmology
 EPrint:
 13 pages, To appear in J. Math. Phys