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 space-times.
- 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
- E-Print:
- 13 pages, To appear in J. Math. Phys