Related papers: Lie symmetries for a conformally flat radiating st…
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 analyze the general model of a radiating star in general relativity. A group analysis of the under determined, nonlinear partial differential equation governing the model's gravitational potentials is performed. This analysis is an…
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 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 obtain solutions of the time-dependent Einstein Field Equations which satisfy the Karmarkar condition via the method of Lie symmetries. Spherically symmetric spacetime metrics are used with metric functions set to impose conformal…
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 analyse the underlying nonlinear partial differential equation which arises in the study of gravitating flat fluid plates of embedding class one. Our interest in this equation lies in discussing new solutions that can be found by means…
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…
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 seek exact solutions to the Einstein field equations which arise when two spacetime geometries are conformally related. Whilst this is a simple method to generate new solutions to the field equations, very few such examples have been…
The present work includes an analytical investigation of a collapsing spherical star in f (R) gravity. The interior of the collapsing star admits a conformal flatness. Information regarding the fate of the collapse is extracted from the…
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…
The spherically symmetric, static spacetime generated by a cross-flow of non-interacting null dust streams can be conveniently interpreted as the radiation atmosphere of a star, which also receives exterior radiation. Formally, such a…
We formulate within a generalized distributional approach the treatment of the stability against radial perturbations for both neutral and charged stratified stars in Newtonian and Einstein's gravity. We obtain from this approach the…
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…
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…
We present a class of conformally flat solutions of the Einstein's field equations for spherical systems undergoing gravitational collapse accompanied with radial heat flux. The interior space-time of the collapsing matter is chosen to be…
We provide a general theoretical framework allowing us to extend the classical Lie theory for partial differential equations to the case of equations of fractional order. We propose a general prolongation formula for the study of Lie…
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…
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…