Collapsing shear-free perfect fluid spheres with heat flow
arXiv:1205.1201 · doi:10.1007/S10714-012-1370-3
Abstract
A global view is given upon the study of collapsing shear-free perfect fluid spheres with heat flow. We apply a compact formalism, which simplifies the isotropy condition and the condition for conformal flatness. This formalism also presents the simplest possible version of the main junction condition, demonstrated explicitly for conformally flat and geodesic solutions. It gives the right functions to disentangle this condition into well known differential equations like those of Abel, Riccati, Bernoulli and the linear one. It yields an alternative derivation of the general solution with functionally dependent metric components. We bring together the results for static and time- dependent models to describe six generating functions of the general solution to the isotropy equation. Their common features and relations between them are elucidated. A general formula for separable solutions is given, incorporating collapse to a black hole or to a naked singularity.
26 pages
References in corpus (17)
- All static spherically symmetric perfect fluid solutions of Einstein's Equations
- Structure and evolution of self-gravitating objects and the orthogonal splitting of the Riemann tensor
- Equilibrium configurations from gravitational collapse
- A causal model of radiating stellar collapse
- Some analytical models of radiating collapsing spheres
- Shear-free radiating collapse and conformal flatness
- Radiating Collapse with Vanishing Weyl stresses
- Spacetime geometry of static fluid spheres
- Relaxational effects in radiating stellar collapse
- Spherical collapse with heat flow and without horizon
- Nonlinear Shear-free Radiative Collapse
- Radiating relativistic matter in geodesic motion
- Spherical collapse of a heat conducting fluid in higher dimensions without horizon
- Self-gravitating spheres of anisotropic fluid in geodesic flow
- New shear-free relativistic models with heat flow
- Evolving spheres of shear-free anisotropic fluid
- Cosmological solutions of the Einstein equation with heat flow
Cited by in corpus (19)
- Analytical study of anisotropic compact star models
- Equilibrium, radial stability and non-adiabatic gravitational collapse of anisotropic neutron stars
- A conformally flat realistic anisotropic model for a compact star
- A different approach to anisotropic spherical collapse with shear and heat radiation
- All solutions for geodesic anisotropic spherical collapse with shear and heat radiation
- Geodesic models generated by Lie symmetries
- Stability and gravitational collapse of neutron stars with realistic equations of state
- Self-similar scalar field collapse
- Conformally Flat Collapsing Stars in f (R) gravity
- Temporal evolution of a radiating star via Lie symmetries
- Collapse of a relativistic self-gravitating star with radial heat flux: Impact of anisotropic stresses
- A class of conformally flat solutions for systems undergoing radiative gravitational collapse
- Higher dimensional charged shear-free relativistic models with heat flux
- New charged shear-free relativistic models with heat flux
- Self Similar Collapse and the Raychaudhuri equation
- Gravitational collapse of anisotropic stars
- Steady heat conduction in general relativity
- On Shearing Fluids with Homogeneous Densities
- Spherically symmetric gravitational collapse in the background of Chaplygin gas