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 (11)

• Spherically symmetric dissipative anisotropic fluids: A general study
• Nonadiabatic charged spherical gravitational collapse
• Transport processes in anisotropic gravitational collapse
• A causal model of radiating stellar collapse
• Some analytical models of radiating collapsing spheres
• Thermal evolution of a radiating anisotropic star with shear
• Shear-free radiating collapse and conformal flatness
• Radiating Collapse with Vanishing Weyl stresses
• Relaxational effects in radiating stellar collapse
• Nonlinear Shear-free Radiative Collapse
• Gravitational Collapse of Self-Similar and Shear-free Fluid with Heat Flow

Cited by in corpus (18)

• Structure and evolution of self-gravitating objects and the orthogonal splitting of the Riemann tensor
• Shearing Expansion-free Spherical Anisotropic Fluid Evolution
• Dynamics of viscous dissipative gravitational collapse: A full causal approach
• Physical causes of energy-density inhomogenization and stability of energy-density homogeneity in relativistic self--gravitating fluids
• Lemaitre-Tolman-Bondi dust spacetimes: Symmetry properties and some extensions to the dissipative case
• 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
• Radiating relativistic matter in geodesic motion
• Generalized Euclidean stars with equation of state
• Geodesic models generated by Lie symmetries
• The role of shear in dissipative gravitational collapse
• Mixed potentials in radiative stellar 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