Related papers: Lie symmetries for a conformally flat radiating st…
We have considered a stationary outflowing envelope from the star accelerated by the radiative force in arbitrary optical depth case. Introduced approximations provide satisfactory description of the behavior of the matter flux with…
A symmetry group classification for fourth-order reaction-diffusion equations, allowing for both second-order and fourth-order diffusion terms, is carried out. The fourth order equations are treated, firstly, as systems of second-order…
We study the underlying nonlinear partial differential equation that governs the behaviour of spherically symmetric charged fluids in general relativity. We investigate the conditions for the equation to admit a first integral or be reduced…
We study non-linear axisymmetric pulsations of rotating relativistic stars using a general relativistic hydrodynamics code under the assumption of a conformal flatness. We compare our results to previous simulations where the spacetime…
We develop a fully relativistic approach for determining the response of a compact star to a time/frequency dependent (tidal) environment. The strategy involves matching the solution for the linearised fluid dynamics in the star's interior…
We develop a numerical algorithm for the solution of the Sturm-Liouville differential equation governing the stationary radial oscillations of nonrotating compact stars. Our method is based on the Numerov's method that turns 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 present a class of exact solutions of Einstein's gravitational field equations describing spherically symmetric and static anisotropic stellar type configurations. The solutions are obtained by assuming a particular form of the…
We present the first results from our new general relativistic, Lagrangian hydrodynamics code, which treats gravity in the conformally flat (CF) limit. The evolution of fluid configurations is described using smoothed particle hydrodynamics…
A system of two cubic reaction-diffusion equations for two independent gene frequencies arising in population dynamics is studied. Depending on values of coefficients, all possible Lie and $Q$-conditional (nonclassical) symmetries are…
Isolated, steady-state galaxies correspond to equilibrium solutions of the Poisson--Vlasov system. We show that (i) all galaxies with a distribution function depending on energy alone must be spherically symmetric and (ii) all axisymmetric…
The spatially conformally flat approximation (CFA) is a viable method to deduce initial conditions for the subsequent evolution of binary neutron stars employing the full Einstein equations. Here we review the status of the original…
The paper considers Euler-Poisson equations which govern the steady state of a self gravitating, rotating, axi-symmetric fluid under the additional assumption that it is incompressible and stratified. In this setting we show that the…
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 develop a simple model for a self-gravitating spherically symmetric relativistic star which begins to collapse from an initially static configuration by dissipating energy in the form of radial heat flow. We utilize the model to show how…
This paper deals with the spherically symmetric self-gravitating star which is considered to be expansion free dissipative perfect fluids distribution. Some recent research reveals that expansion free dynamical star must be accelerating and…
In the paper we discuss equilibrium states of stars, using a simplified analytic model. A star is considered as self-graviting body of gas. We use a condition for the equilibrium state of the body in the form of a differential equation,…
We model the physical behaviour at the surface of a relativistic radiating star in the strong gravity limit. The spacetime in the interior is taken to be spherically symmetrical and shear-free. The heat conduction in the interior of the…
Lie symmetry analysis is applied to study the nonlinear rotating shallow water equations. The 9-dimensional Lie algebra of point symmetries admitted by the model is found. It is shown that the rotating shallow water equations are related…
We derive the Lie point symmetries for the MIT Bag Model for quark stars in relativistic astrophysics. Four cases of reduction arise; three cases of specific values of the measure of the anisotropy variation, and one general case, which we…