Related papers: Radiating stars with exponential Lie symmetries
We consider the general case of an accelerating, expanding and shearing model of a radiating relativistic star using Lie symmetries. We obtain the Lie symmetry generators that leave the equation for the junction condition invariant, and…
We systematically analyze the nonlinear partial differential equation that determines the behaviour of a bounded radiating spherical mass in general relativity. Four categories of solution are possible. These are identified in terms of…
We consider a relativistic radiating spherical star in conformally flat spacetimes. In particular we study the junction condition relating the radial pressure to the heat flux at the boundary of the star which is a nonlinear partial…
A systematic analysis of the junction condition, relating the radial pressure with the heat flow in a shear-free relativistic radiating star, is undertaken. This is a highly nonlinear partial differential equation in general. We obtain the…
We study the behaviour of a radiating star when the interior expanding, shearing fluid particles are traveling in geodesic motion. We demonstrate that it is possible to obtain new classes of exact solutions in terms of elementary functions…
We study the temporal equation of radiating stars by using three powerful methods for the analysis of nonlinear differential equations. Specifically, we investigate the global dynamics for the given master ordinary differential equation to…
It is proposed to use the Lie group theory of symmetries of differential equations to investigate the system of equations describing a static star in a radiative and convective equilibrium. It is shown that the action of an admissible group…
We study the gravitational behaviour of a spherically symmetric radiating star when the fluid particles are in geodesic motion. We transform the governing equation into a simpler form which allows for a general analytic treatment. We find…
We consider a radiating shear-free spherically symmetric metric in higher dimensions. Several new solutions to the Einstein's equations are found systematically using the method of Lie analysis of differential equations. Using the five Lie…
We investigate the evolution of the surface of radiating stars by studying the asymptotic behaviour of exact solutions initiated via the stationary boundary condition. This boundary condition leads to a master equation in the form of a…
In a series of articles we describe a novel class of geometrical models of relativistic stars. Our approach to the static spherically symmetric solutions of Einstein equations is based on a careful physical analysis of radial gauge…
We study realistic models of relativistic radiating stars undergoing gravitational collapse which have vanishing Weyl tensor components. Previous investigations are generalised by retaining the inherent nonlinearity at the boundary. We…
It is shown that the expressions for the tangential pressure, the anisotropy factor and the radial pressure in the Einstein equations may serve as generating functions for stellar models. The latter can incorporate an equation of state when…
We investigate the behaviour of a relativistic spherically symmetric radiative star with an accelerating, expanding and shearing interior matter distribution in the presence of anisotropic pressures. The junction condition can be written in…
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…
We study the junction condition relating the pressure to the heat flux at the boundary of a shearing and expanding spherically symmetric radiating star when the fluid particles are travelling in geodesic motion. The Lie symmetry generators…
We model the gravitational behaviour of a radiating star when the exterior geometry is the generalised Vaidya spacetime. The interior matter distribution is shear-free and undergoing radial heat flow. The exterior energy momentum tensor is…
The paper considers Euler-Poisson equations which govern the steady state of a self gravitating, rotating, axi-symmetric stars under the additional assumption that it is composed of incompressible stratified fluid. The original system of…
We describe a novel class of geometrical models of relativistic stars. Our approach to the static spherically symmetric solutions of Einstein equations is based on a careful physical analysis of radial gauge conditions. It brings us to a…
We introduce a model concerning radiational gaseous stars and establish the existence theory of stationary solutions to the free boundary problem of hydrostatic equations describing the radiative equilibrium. We also concern the local…