scholarly journals An interior solution with perfect fluid

2020 ◽  
Vol 35 (17) ◽  
pp. 2050141 ◽  
Author(s):  
Joaquin Estevez-Delgado ◽  
Jose Vega Cabrera ◽  
Joel Arturo Rodriguez Ceballos ◽  
Arthur Cleary-Balderas ◽  
Mauricio Paulin-Fuentes
Keyword(s):  
Perfect Fluid ◽  
Speed Of Sound ◽  
Numerical Data ◽  
Index Formula ◽  
Interior Solution ◽  
Radial Coordinate ◽  
Speed Of Light ◽  
Bounded Functions ◽  
The Stability ◽  
Stability Of The Solution

Starting from the construction of a solution for Einstein’s equations with a perfect fluid for a static spherically symmetric spacetime, we present a model for stars with a compactness rate of [Formula: see text]. The model is physically acceptable, that is to say, its geometry is non-singular and does not have an event horizon, pressure and speed of sound are bounded functions, positive and monotonically decreasing as function of the radial coordinate, also the speed of sound is lower than the speed of light. While it is shown that the adiabatic index [Formula: see text], which guarantees the stability of the solution. In a complementary manner, numerical data are presented considering the star PSR J0737-3039A with observational mass of [Formula: see text], for the value of compactness [Formula: see text], which implies the radius [Formula: see text] and the range of the density [Formula: see text] [Formula: see text], where [Formula: see text] and [Formula: see text] are the central density and the surface density, respectively. This range is consistent with the expected values; as such, the model presented allows to describe this type of stars.

A uniparametric perfect fluid solution to represent compact stars

2021 ◽  
Vol 36 (10) ◽  
pp. 2150068
Author(s):  
Joaquin Estevez-Delgado ◽  
Noel Enrique Rodríguez Maya ◽  
José Martínez Peña ◽  
David Rivera Rangel ◽  
Nancy Cambron Muñoz
Keyword(s):  
Neutron Stars ◽  
Perfect Fluid ◽  
Stellar Model ◽  
Compact Objects ◽  
Compact Stars ◽  
Index Formula ◽  
Perfect Fluid Solution ◽  
Gravitational Theories ◽  
State Formula ◽  
The Stability

In the description of neutron stars, it is very important to consider gravitational theories as general relativity, due to the determining influence on the behavior of the different types of stars, since some objects show densities even bigger than nuclear density. This paper starts with Einstein’s equations for a perfect fluid and then we present a uniparametric stellar model which allows to describe compact objects like neutron stars with compactness ratio [Formula: see text]. The pressure and density are monotone decreasing regular functions, the speed of sound satisfies the causality condition, while the value for its adiabatic index [Formula: see text] guarantees the stability. In addition, the graph of [Formula: see text] versus [Formula: see text] shows a quasi-linear relationship for the equation of state [Formula: see text], which is similar to the so-called MIT Bag equation when we have the interaction between quarks. In our case it is due to the interaction of the different components found inside the star, such as electrons and neutrons. As an application of the model, we describe the star PSR J1614-2230 with a observed mass of [Formula: see text] and a radius [Formula: see text], the model shows that the maximum central density occurs for a maximal compactness value [Formula: see text].

scholarly journals The relativistic incompressible sphere

1968 ◽  
Vol 8 (1) ◽  
pp. 6-16 ◽  
Author(s):  
H. A. Buchdahl ◽  
W. J. Land
Keyword(s):  
Speed Of Sound ◽  
Interior Solution ◽  
Natural Analogue ◽  
Speed Of Light ◽  
Static Sphere

SummaryThe Schwarzschild Interior Solution represents a static sphere the proper density of which has the same value throughout. Though it is sometimes referred to as an “incompressible” sphere it is physically unacceptable since (formally) the speed of sound within it is infinite. Perhaps the most natural analogue of the classical incompressible sphere is therefore a sphere such that the speed of sound is everywhere just equal to the speed of light. This paper investigates spheres of this kind in some detail.

Static critical behaviors in random-spin systems with short-range interaction

1978 ◽  
Vol 56 (1) ◽  
pp. 139-148 ◽  
Author(s):  
Yoshitake Yamazaki
Keyword(s):  
Short Range ◽  
Spin Systems ◽  
Three Dimensions ◽  
Index Formula ◽  
Spin Component ◽  
Renormalization Group Theory ◽  
Short Range Interaction ◽  
Range Interaction ◽  
The Stability ◽  
Component Models

Critical behaviors in quenched random-spin systems with N-spin component are studied in the limit M → 0 of the non-random MN-component models by means of the renormalization group theory. As the static critical phenomena the stability of the fixed points is investigated and the critical exponents η[~ O(ε3); ε ≡ 4 – d], γ, α, and crossover index [Formula: see text] and the equation of state [~ O(ε)] are obtained. Within the approximation up to the order ε2, even the random-spin systems with N = 2 or 3 are unstable in the three dimensions and the pure systems are stable there.

An anisotropic charged fluids with Chaplygin equation of state

2021 ◽  
Vol 36 (21) ◽  
pp. 2150153
Author(s):  
Joaquin Estevez-Delgado ◽  
Noel Enrique Rodríguez Maya ◽  
José Martínez Peña ◽  
Arthur Cleary-Balderas ◽  
Jorge Mauricio Paulin-Fuentes
Keyword(s):  
Speed Of Sound ◽  
Radial Pressure ◽  
State Equation ◽  
Stellar Model ◽  
Compact Objects ◽  
Anisotropic Fluid ◽  
The Stability ◽  
Electrically Charged ◽  
Chaplygin Equation ◽  
Graphic Description

A stellar model with an electrically charged anisotropic fluid as a source of matter is presented. The radial pressure is described by a Chaplygin state equation, [Formula: see text], while the anisotropy [Formula: see text] is annulled in the center of the star [Formula: see text] is regular and [Formula: see text], the electric field, is also annulled in the center. The density pressures and the tangential speed of sound are regular, while the radial speed of sound is monotonically increasing. The model is physically acceptable and meets the stability criteria of Harrison–Zeldovich–Novikov and in respect of the cracking concept the solution is unstable in the region of the center and potentially stable near the surface. A graphic description is presented for the case of an object with a compactness rate [Formula: see text], mass [Formula: see text] and radius [Formula: see text] km that matches the star Vela X-1. Also, the interval of the central density [Formula: see text], which is consistent with the expected magnitudes for this type of stars, which shows that the behavior is accurate for describing compact objects.

scholarly journals CALCULATION OF A JET ENGINE IN A COMPLEX PLANE USING A ONE-DIMENSIONAL SOLUTION OF THE NAVIER-STOKES EQUATION

2021 ◽  
Vol 7 (1(37)) ◽  
pp. 9-22
Author(s):  
E.G. Yakubovsky
Keyword(s):  
Speed Of Sound ◽  
Added Mass ◽  
Navier Stokes ◽  
Speed Of Light ◽  
Attached Mass ◽  
Additional Mass ◽  
Navier Stokes Equation ◽  
Dimensional Solution ◽  
Jet Engine ◽  
One Dimensional

This article proposes an algorithm to describe the motion of a body in the atmosphere using the added mass. Attached mass is the property of a medium to form additional mass, as I assume with a relativistic denominator at the speed of sound instead of the speed of light. Newton’s second law for added mass assumes two terms with the same speed, one is relativistic at the speed of light, and the other is attached mass with a relativistic denominator at the speed of sound. The use of a relativistic denominator with the speed of sound is a new idea that allows, according to well-known formulas with added mass, which is valid at low speeds of a body, to describe

Charged gravastars in f(R,T,RμνTμν) gravity

2021 ◽  
pp. 2150084
Author(s):  
Z. Yousaf ◽  
M. Z. Bhatti
Keyword(s):  
Perfect Fluid ◽  
Energy Momentum Tensor ◽  
Equations Of State ◽  
Mathematical Formulation ◽  
Momentum Tensor ◽  
Spherically Symmetric ◽  
De Sitter ◽  
The Stability ◽  
Physical Features ◽  
Modified Theory

We explore the aspects of the electromagnetism on the stability of gravastar in a particular modified theory, i.e. [Formula: see text] where [Formula: see text], [Formula: see text] is the Ricci scalar and [Formula: see text] is the trace of energy–momentum tensor. We assume a spherically symmetric static metric coupled comprising of perfect fluid in the presence of electric charge. The purpose of this paper is to extend the results of [S. Ghosh, F. Rahaman, B. K. Guha and S. Ray, Phys. Lett. B 767 (2017) 380.] to highlight the effects of [Formula: see text] gravity in the formation of charged gravastars. We demonstrated the mathematical formulation, utilizing different equations of state, for the three respective regions (i.e. inner, shell, exterior) of the gravastar. We have matched smoothly the interior de Sitter and the exterior Reissner–Nordström metric at the hypersurface. At the end we extracted few conclusions by working on the physical features of the charged gravastar, mathematically and graphically.

scholarly journals Dynamics of a Discretization Physiological Control System

2007 ◽  
Vol 2007 ◽  
pp. 1-16 ◽  
Author(s):  
Xiaohua Ding ◽  
Huan Su
Keyword(s):  
Control System ◽  
Discrete System ◽  
Numerical Results ◽  
Positive Equilibrium ◽  
Hopf Bifurcations ◽  
Physiological Control ◽  
Midpoint Rule ◽  
The Stability ◽  
Stability Of The Solution

We study the dynamics of solutions of discrete physiological control system obtained by Midpoint rule. It is shown that a sequence of Hopf bifurcations occurs at the positive equilibrium as the delay increases and we analyze the stability of the solution of the discrete system and calculate the direction of the Hopf bifurcations. The numerical results are presented.

Charged perfect fluid stellar structures with Bardeen model

2020 ◽  
Vol 35 (18) ◽  
pp. 2050083 ◽  
Author(s):  
M. Farasat Shamir ◽  
G. Mustafa ◽  
Quresha Hanif
Keyword(s):  
Electric Field ◽  
Perfect Fluid ◽  
Maxwell Equations ◽  
Graphical Analysis ◽  
Physical Parameters ◽  
Symmetric Model ◽  
Speed Of Light ◽  
Suitable Form ◽  
Model Geometry ◽  
Spherically Symmetric Model

This paper is devoted to study static spherically symmetric model in the presence of charged perfect fluid. This is the generalization of neutral perfect fluid (when there is no charge) through the solution of Einstein Maxwell equations. For this purpose, we consider a suitable form of gravitational potential [Formula: see text] and the electric field [Formula: see text], already used in the literature. The value of mass-radius ratio or compactness [Formula: see text], which depends upon the chosen model exceeds the value [Formula: see text] corresponding to neutral stars. The most important feature of the current study is to use the Bardeen model geometry instead of usual Reissner–Nordström model for the matching conditions. In this case the energy density and pressure remain positive, bounded and monotonically decreasing whereas electric field is monotonically increasing. Also the causality condition, i.e. the magnitude of speed of sound must be less than the speed of light, is satisfied. Moreover, the behavior of all the physical parameters at the center and on surface of star of mass [Formula: see text] and for Her X-1 are tabulated. All the results by graphical analysis and tabular information suggest that Bardeen model provides physically realistic stellar structures.

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