A Riccati equation in radiative stellar collapse

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

References in corpus (3)

• Nonadiabatic charged spherical gravitational collapse
• Some analytical models of radiating collapsing spheres
• Nonlinear Shear-free Radiative Collapse

Cited by in corpus (14)

• Shearing Expansion-free Spherical Anisotropic Fluid Evolution
• Dynamics of viscous dissipative gravitational collapse: A full causal approach
• Radiating stars with generalised Vaidya atmospheres
• Shearing radiative collapse with expansion and acceleration
• A different approach to anisotropic spherical collapse with shear and heat radiation
• All solutions for geodesic anisotropic spherical collapse with shear and heat radiation
• Generalized Euclidean stars with equation of state
• Radiating relativistic matter in geodesic motion
• Geodesic models generated by Lie symmetries
• The role of shear in dissipative gravitational collapse
• Thermal Behaviour of Euclidean Stars
• New shear-free relativistic models with heat flow
• Gravitational collapse for a radiating anisotropic fluid
• Integrability of Lie systems through Riccati equations