Related papers: A self-similar dynamics in viscous spheres
We study the effect of transport processes (diffusion and free--streaming) on a collapsing spherically symmetric distribution of matter in a self--similar space--time. A very simple solution shows interesting features when it is matched…
The scale-free nature of gravitational interaction in both Newtonian gravity and the general theory of relativity gives rise to the concept of self-similarity, where solutions are scale invariant. As a result of this property, the governing…
We apply the post-quasi--static approximation, an iterative method for the evolution of self-gravitating spheres of matter, to study the evolution of anisotropic non-adiabatic radiating and dissipative distributions in General Relativity.…
Self-similar, spherically symmetric cosmological models with a perfect fluid and a scalar field with an exponential potential are investigated. New variables are defined which lead to a compact state space, and dynamical systems methods are…
A recent study of dissipative collapse considered a contracting sphere in which the areal and proper radii are equal throughout its evolution. The interior spacetime was matched to the exterior Vaidya spacetime which generated a temporal…
Here we study some general properties of spherical shear-free collapse. Its general solution when imposing conformal flatness is reobtained [1,2] and matched to the outgoing Vaidya spacetime. We propose a simple model satisfying these…
A model is proposed of a collapsing quasi-spherical radiating star with matter content as shear-free isotropic fluid undergoing radial heat-flow with outgoing radiation. To describe the radiation of the system, we have considered both plane…
Considering charged fluid spheres as anisotropic sources and the diffusion limit as the transport mechanism, we suppose that the inner space--time admits self--similarity. Matching the interior solution with the…
A self-similar solution for time evolution of isothermal, self-gravitating viscous disks is found under the condition that $\alpha' \equiv \alpha (H/r)$ is constant in space (where $\alpha$ is the viscosity parameter and $H/r$ is the ratio…
We analyze the problem of gravitational collapse considering the matching of an exterior region described by the Vaidya's metric and an interior region described by a spherically symmetric shear-free inhomogeneous geometry sourced by a…
A dynamical symmetry for spherical collapse has been studied using a linear transformation of the initial data set (mass and kinetic energy function) and the area radius. With proper choice of the initial area radius, the evolution as well…
The Sturm-Liouville eigenvalue equation for eigenmodes of the radial oscillations is determined for spherically symmetric perfect fluid configurations in spacetimes with a nonzero cosmological constant and applied in the cases of…
Models of active nematics in biological systems normally require complexity arising from the hydrodynamics involved at the microscopic level as well as the viscoelastic nature of the system. Here we show that a minimal, space-independent,…
Perfect fluid spacetimes admitting a kinematic self-similarity of infinite type are investigated. In the case of plane, spherically or hyperbolically symmetric space-times the field equations reduce to a system of autonomous ordinary…
A new dynamical solution for a gas sphere under self-gravity is presented to describe a development of a gas sphere from a motion-less state to a state of expansion with a constant speed and a reflection phenomenon in the dynamics of the…
We seek for self-similar solutions describing the time-dependent evolution of self-gravity systems with either spherical symmetry or axisymmetric disk geometry. By assuming self-similar variable $x\equiv r/at$ where $a$ is isothermal sound…
We consider a spherically symmetric stellar model in general relativity whose interior consists of a pressureless fluid undergoing microscopic velocity diffusion in a cosmological scalar field. We show that the diffusion dynamics compel the…
We evolve nonadiabatic charged spherical distributions of matter. Dissipation is described by the free-streaming approximation. We match a self-similar interior solution with the Reissner-Nordstr\"om-Vaidya exterior solution. The transport…
We investigate the gravitational collapse of a massive scalar field in a conformally flat, spherically symmetric spacetime within general relativity. The collapsing matter distribution is modeled using a minimally coupled homogeneous scalar…
We study the general properties of fluid spheres satisfying the heuristic assumption that their areas and proper radius are equal (the Euclidean condition). Dissipative and non-dissipative models are considered. In the latter case, all…