scholarly journals Framework for generalized polytropes with complexity factor

2019 ◽  
Vol 79 (12) ◽  
Author(s):  
Shiraz Khan ◽  
S. A. Mardan ◽  
M. A. Rehman
Keyword(s):  
Equation Of State ◽  
Energy Density ◽  
Differential Equations ◽  
Spherical Symmetry ◽  
Mass Density ◽  
Fluid Distribution ◽  
System Of Differential Equations ◽  
Systems Of Differential Equations ◽  
Polytropic Equation

AbstractA framework is developed for generalized polytropes with the help of complexity factor introduced by Herrera (Phy Rev D 97:044010, 2018), by using the spherical symmetry with anisotropic inner fluid distribution. For this purpose generalized polytropic equation of state will be used, having two cases (i) for mass density $$(\mu _{o})$$(μo), (ii) for energy density $$(\mu )$$(μ), each case leads to a system of differential equations. These systems of differential equations involve two equations with three unknowns and they will be made consistent by using the complexity factor. The analysis of the solutions of these systems will be carried out graphically by using different parametric values involved in the systems.

scholarly journals Study of generalized cylindrical polytropes with complexity factor

2021 ◽  
Vol 81 (9) ◽  
Author(s):  
Shiraz Khan ◽  
S. A. Mardan ◽  
M. A. Rehman
Keyword(s):  
Equation Of State ◽  
Energy Density ◽  
Differential Equations ◽  
Mass Density ◽  
Modify Form ◽  
Graphical Analysis ◽  
Fluid Distribution ◽  
Anisotropic Fluid ◽  
Polytropic Equation ◽  
Frame Work

AbstractIn this paper, complexity factor is used with generalized polytropic equation of state to develop two consistent systems of three differential equations and a general frame work is established for modify form of Lane-Emden equations. For this purpose anisotropic fluid distribution is considered in cylindrical static symmetry with two cases of generalized polytropic equation of state (i) mass density $$\mu _{o}$$ μ o and (ii) energy density $$\mu $$ μ . A graphical analysis will be carried out for the numerical solution of these systems of three differential equations.

OF CHARGED STARS AND CHARGED BLACK HOLES

2004 ◽  
Vol 13 (07) ◽  
pp. 1375-1379 ◽  
Author(s):  
MANUEL MALHEIRO ◽  
RODRIGO PICANÇO ◽  
SUBHARTHI RAY ◽  
JOSÉ P. S. LEMOS ◽  
VILSON T. ZANCHIN
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Charged Particle ◽  
Equation Of State ◽  
Mass Density ◽  
Compact Star ◽  
Maximum Amount ◽  
Stellar Structure ◽  
Charged Black Holes ◽  
Polytropic Equation

Effect of maximum amount of charge a compact star can hold, is studied here. We analyze the different features in the renewed stellar structure and discuss the reasons why such huge charge is possible inside a compact star. We studied a particular case of a polytropic equation of state (EOS) assuming the charge density is proportional to the mass density. Although the global balance of force allows a huge charge, the electric repulsion faced by each charged particle forces it to leave the star, resulting in the secondary collapse of the system to form a charged black hole.

scholarly journals DARK ENERGY IN GLOBAL BRANE UNIVERSE

2007 ◽  
Vol 16 (10) ◽  
pp. 1633-1640 ◽  
Author(s):  
YONGLI PING ◽  
LIXIN XU ◽  
CHENGWU ZHANG ◽  
HONGYA LIU
Keyword(s):  
Dark Energy ◽  
Equation Of State ◽  
Energy Density ◽  
Exact Solutions ◽  
Deceleration Parameter ◽  
Mass Density ◽  
Density Parameter ◽  
Dark Energy Density ◽  
Friedmann Equations

We discuss the exact solutions of brane universes and the results indicate that the Friedmann equations on the branes are modified with a new density term. Then, we assume the new term as the density of dark energy. Using Wetterich's parametrization equation of state (EOS) of dark energy, we obtain that the new term varies with the redshift z. Finally, the evolutions of the mass density parameter Ω2, dark energy density parameter Ωx and deceleration parameter q2 are studied.

scholarly journals Study of dynamics of bilinear systems with parameter

2021 ◽  
Vol 80 (2) ◽  
pp. 47-54
Author(s):  
L. Kh. Zhunussova ◽  
Keyword(s):  
Numerical Calculation ◽  
Differential Equations ◽  
Bilinear System ◽  
Bilinear Systems ◽  
System Of Differential Equations ◽  
Systems Of Differential Equations ◽  
Computational Processes

A number of problems in biology, ecology and chemistry can be reduced to the consideration of n-dimensional nonlinear, in particular, bilinear systems of differential equations containing a parameter. For such systems, it is of interest to find a solution to the influence of a parameter. Complex computational processes arising in the modeling of the above systems make it possible for research on this topic to remain always relevant. In this paper, a bilinear system of differential equations is considered. The numerical calculation of the solution of this system is presented.

scholarly journals GRAVITATIONAL LENSING STATISTICS AS A PROBE OF DARK ENERGY

2000 ◽  
Vol 15 (16) ◽  
pp. 1023-1029 ◽  
Author(s):  
ZONG-HONG ZHU
Keyword(s):  
Dark Energy ◽  
Equation Of State ◽  
Energy Density ◽  
Cosmological Model ◽  
Gravitational Lensing ◽  
Mass Density ◽  
Density Parameter ◽  
Dark Energy Density ◽  
Analytic Expression ◽  
Cosmic Mass

By using the comoving distance, we derive an analytic expression for the optical depth of gravitational lensing, which depends on the redshift to the source and the cosmological model characterized by the cosmic mass density parameter Ωm, the dark energy density parameter Ωm and its equation of state ωx = px/ρx. It is shown that, the larger the dark energy density and the more negative its pressure, the higher is the gravitational lensing probability. This fact can provide an independent constraint for dark energy.

scholarly journals Bilateral approximations and periodic solutions of systems of differential equations with impulses

1985 ◽  
Vol 31 (2) ◽  
pp. 293-307
Author(s):  
S.G. Hristova ◽  
D.D. Bainov
Keyword(s):  
Periodic Solution ◽  
Linear System ◽  
Differential Equations ◽  
Periodic Solutions ◽  
System Of Differential Equations ◽  
Systems Of Differential Equations ◽  
Non Linear ◽  
Impulsive Perturbations ◽  
Non Linear System

The paper justifies a method of bilateral approximations for finding the periodic solution of a non-linear system of differential equations with impulsive perturbations at fixed moments of time.

Self-gravitating fluids

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Equation Of State ◽  
Velocity Field ◽  
Spherical Symmetry ◽  
Continuity Equation ◽  
Mass Density ◽  
Emden Equation ◽  
Barotropic Fluid ◽  
Perfect Fluids ◽  
The Poisson Equation ◽  
Equilibrium Configurations

This chapter briefly describes ‘perfect fluids’. These are characterized by their mass density ρ‎(t, xⁱ), pressure p(t, ⁱ), and velocity field v(t, ⁱ). The motion and equilibrium configurations of these fluids are determined by the equation of state, for example, p = p(ρ‎) for a barotropic fluid, and by the gravitational potential U(t, ⁱ) created at a point ⁱ by other fluid elements. The chapter shows that, given an equation of state, the equations of the problem to be solved are the continuity equation, the Euler equation, and the Poisson equation. It then considers static models with spherical symmetry, as well as polytropes and the Lane–Emden equation. Finally, the chapter studies the isothermal sphere and Maclaurin spheroids.

scholarly journals CHARGED POLYTROPIC STARS AND A GENERALIZATION OF LANE–EMDEN EQUATION

2004 ◽  
Vol 13 (07) ◽  
pp. 1441-1445 ◽  
Author(s):  
RODRIGO PICANÇO ◽  
MANOEL MALHEIRO ◽  
SUBHARTHI RAY
Keyword(s):  
Equation Of State ◽  
Differential Equations ◽  
Electric Field ◽  
Boundary Conditions ◽  
Radial Component ◽  
Spherically Symmetric ◽  
Field Equations ◽  
Emden Equation ◽  
Polytropic Equation ◽  
Structure Equations

In this paper we discuss charged stars with polytropic equation of state, where we derive an equation analogous to the Lane–Endem equation. We assume that these stars are spherically symmetric, and the electric field have only the radial component. First we review the field equations for such stars and then we proceed with the analog of the Lane–Emden equation for a polytropic Newtonian fluid and their relativistic equivalent (Tooper, 1964).1 These kind of equations are very interesting because they transform all the structure equations of the stars in a group of differential equations which are much more simple to solve than the source equations. These equations can be solved numerically for some boundary conditions and for some initial parameters. For this we assume that the pressure caused by the electric field obeys a polytropic equation of state too.

The Solution of Non-Homogeneous Systems of Differential Equations by Undetermined Coefficients

1966 ◽  
Vol 9 (4) ◽  
pp. 481-487
Author(s):  
Fred Brauer
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Linear Algebra ◽  
Single Equation ◽  
Analogous Problem ◽  
System Of Differential Equations ◽  
Homogeneous Differential Equation ◽  
Homogeneous Systems ◽  
Systems Of Differential Equations ◽  
Straightforward Extension

The solution of a linear non-homogeneous differential equation whose non-homogeneous term is of the form tkeαt can be obtained by what is usually called the method of undetermined coefficients. The application of this method may be justified in several different ways (see for example [1, pp. 114–117], [2, pp. 94–99], [3]).We shall consider the analogous problem for a system of differential equations. It turns out that we can solve this problem using only elementary techniques of linear algebra. The solution has essentially the same form as in the case of a single equation, but may contain terms which would not be expected and may lack terms which would be expected in a straightforward extension of the theory to systems. Our method of obtaining the solution is constructive, in the sense that while our results give only the form of the solution, the solution itself may be found by substitution of this form into the system of differential equations.

scholarly journals Hyperbolically Symmetric Versions of Lemaitre–Tolman–Bondi Spacetimes

Entropy ◽  
2021 ◽  
Vol 23 (9) ◽  
pp. 1219
Author(s):  
Luis Herrera ◽  
Alicia Di Prisco ◽  
Justo Ospino
Keyword(s):  
Equation Of State ◽  
Energy Density ◽  
Spherical Symmetry ◽  
Anisotropic Pressure ◽  
Common Features ◽  
Stiff Equation ◽  
All Solutions

We study fluid distributions endowed with hyperbolic symmetry, which share many common features with Lemaitre–Tolman–Bondi (LTB) solutions (e.g., they are geodesic, shearing, and nonconformally flat, and the energy density is inhomogeneous). As such, they may be considered as hyperbolic symmetric versions of LTB, with spherical symmetry replaced by hyperbolic symmetry. We start by considering pure dust models, and afterwards, we extend our analysis to dissipative models with anisotropic pressure. In the former case, the complexity factor is necessarily nonvanishing, whereas in the latter cases, models with a vanishing complexity factor are found. The remarkable fact is that all solutions satisfying the vanishing complexity factor condition are necessarily nondissipative and satisfy the stiff equation of state.

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