RELATIVISTIC EFFECTS IN POLYTROPIC COMPACT STARS

2007 ◽  
Vol 16 (09) ◽  
pp. 2834-2837 ◽  
Author(s):  
L. FERRARI ◽  
G. ESTRELA ◽  
M. MALHEIRO
Keyword(s):  
Equation Of State ◽  
Relativistic Effects ◽  
Fermi Gas ◽  
Matter Density ◽  
Compact Stars ◽  
Polytropic Index ◽  
First Order ◽  
Polytropic Equation ◽  
Relativistic Fermi ◽  
First Order Differential Equations

We solve numerically the two first order differential equations obtained by Tooper for polytropic compact stars. These equations depend on the polytropic index n related to the adiabatic index Γ = 1 + 1/n and on a parameter σ that manifests the relativistic content of the polytropic equation of state (EOS). In this work we investigate the effect of increasing σ for two polytropic EOS: the case of a nonrelativistic Fermi gas (n = 1.5) and the relativistic one (n = 3.0). We show that for large values of σ, where the sound velocity is not small in comparison to the velocity of light, the matter density is more concentrated in the center of the star and as a consequence the star mass also is: this effect is quite strong in the case of the relativistic fermi gas.

scholarly journals Impact of generalized polytropic equation of state on charged anisotropic polytropes

2020 ◽  
Vol 80 (2) ◽  
Author(s):  
S. A. Mardan ◽  
M. Rehman ◽  
I. Noureen ◽  
R. N. Jamil
Keyword(s):  
Equation Of State ◽  
Speed Of Sound ◽  
Graphical Analysis ◽  
Maxwell Field ◽  
Anisotropic Fluid ◽  
Polytropic Index ◽  
Model Parameters ◽  
Field Equations ◽  
Polytropic Equation ◽  
Fluid Configuration

Abstract In this paper, generalized polytropic equation of state is used to get new classes of polytropic models from the solution of Einstein-Maxwell field equations for charged anisotropic fluid configuration. The models are developed for different values of polytropic index $$n=1,~\frac{1}{2},~2$$n=1,12,2. Masses and radii of eight different stars have been regained with the help of developed models. The speed of sound technique and graphical analysis of model parameters is used for the viability of developed models. The analysis of models indicates they are well behaved and physically viable.

DARK ENERGY WITH POLYTROPIC EQUATION-OF-STATE

2008 ◽  
Vol 23 (37) ◽  
pp. 3187-3198 ◽  
Author(s):  
UTPAL MUKHOPADHYAY ◽  
SAIBAL RAY ◽  
S. B. DUTTA CHOUDHURY
Keyword(s):  
Dark Energy ◽  
Equation Of State ◽  
Closed Form ◽  
State Parameter ◽  
Phantom Energy ◽  
Polytropic Index ◽  
Closed Form Solutions ◽  
Real Nature ◽  
Equation Of State Parameter ◽  
Polytropic Equation

Equation-of-state parameter plays a significant role for guessing the real nature of dark energy. Here polytropic equation-of-state p = ωρnis chosen for some of the kinematical Λ-models viz., [Formula: see text], [Formula: see text] and Λ ~ ρ. Although in dust cases (ω = 0) closed form solutions show no dependency on the polytropic index n, but in non-dust situations some new possibilities are opened up including phantom energy with supernegative (ω < -1) equation-of-state parameter.

THERMOSTATISTIC PROPERTIES OF A RELATIVISTIC FERMI GAS

2010 ◽  
Vol 24 (29) ◽  
pp. 5783-5792 ◽  
Author(s):  
SHUKUAN CAI ◽  
GUOZHEN SU ◽  
JINCAN CHEN
Keyword(s):  
Heat Capacity ◽  
Pair Production ◽  
Low Temperatures ◽  
Chemical Potential ◽  
Dimensional Space ◽  
Average Distance ◽  
Relativistic Effects ◽  
Fermi Gas ◽  
Compton Wavelength ◽  
Relativistic Fermi

Thermodynamic properties of a relativistic Fermi gas in any dimensional space are studied, in which the influence of particle–antiparticle pair production is taken into account. It is shown that relativistic effects cannot be ignored even at very low temperatures for the system with the Compton wavelength of a particle comparable with the average distance between particles. The pair production results in some novel characteristics, which include the asymptotic behavior of the chemical potential and the rapid increase in the heat capacity with temperature in the high temperature regions, etc.

Possible radii of compact stars: A relativistic approach

2016 ◽  
Vol 31 (40) ◽  
pp. 1650219 ◽  
Author(s):  
Mehedi Kalam ◽  
Sk Monowar Hossein ◽  
Sajahan Molla
Keyword(s):  
Equation Of State ◽  
Neutron Stars ◽  
Observational Data ◽  
Matter Density ◽  
Compact Stars ◽  
X Ray ◽  
Relativistic Approach ◽  
Points Of View ◽  
X Ray Binaries ◽  
Surface Redshift

The inner structure of compact stars is checked from theoretical as well as observational points of view. In this paper, we determine the possible radii of six compact stars: two binary millisecond pulsars, namely PSR J1614-2230 and PSR J1903+327, studied by [P. B. Demorest, T. Pennucci, S. M. Ransom, M. S. E. Roberts and W. T. Hessels, Nature 467, 1081 (2010)] and four X-ray binaries, namely Cen X-3, SMC X-1, Vela X-1 and Her X-1 studied by [M. L. Rawls et al., Astrophys. J. 730, 25 (2011)]. Interestingly, we see that density of the star does not vanishes at the boundary though it is maximum at the center which implies that these compact stars may be treated as strange stars rather than neutron stars. We propose a stiff equation of state (EoS) relating to pressure with matter density. We also obtain compactness (u) and surface redshift (Z[Formula: see text]) for the above-mentioned stars and compare it with the recent observational data.

Cracking in anisotropic polytropic models

2018 ◽  
Vol 33 (24) ◽  
pp. 1850139
Author(s):  
M. Sharif ◽  
Sobia Sadiq
Keyword(s):  
Distribution Function ◽  
Equation Of State ◽  
Anisotropic Fluid ◽  
Polytropic Index ◽  
Force Distribution ◽  
Spherically Symmetric ◽  
Field Equations ◽  
Polytropic Equation ◽  
Density Perturbations ◽  
Fluid Configuration

This paper is devoted to examine the cracking of spherically symmetric anisotropic fluid configuration for polytropic equation of state. For this purpose, we formulate the corresponding field equations as well as generalized Tolman–Oppenheimer–Volkoff equation. We introduce density perturbations in matter variables and then construct the force distribution function. In order to examine the occurrence of cracking/overturning, we consider two models corresponding to two values of the polytropic index. It is found that the first model exhibits overturning for the considered values of polytropic constant while the second model neither exhibits cracking nor overturning for larger values of polytropic constant.

Asymptotics for third-order nonlinear differential equations: Non-oscillatory and oscillatory cases

2021 ◽  
pp. 1-19
Author(s):  
Calogero Vetro ◽  
Dariusz Wardowski
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Order Differential Equation ◽  
Nonlinear Differential Equations ◽  
Oscillatory Behavior ◽  
Third Order ◽  
First Order ◽  
Third Order Differential Equation ◽  
Comparison Technique ◽  
First Order Differential Equations

We discuss a third-order differential equation, involving a general form of nonlinearity. We obtain results describing how suitable coefficient functions determine the asymptotic and (non-)oscillatory behavior of solutions. We use comparison technique with first-order differential equations together with the Kusano–Naito’s and Philos’ approaches.

QCD constraints on the equation of state for compact stars

2016 ◽  
Vol 956 ◽  
pp. 813-816
Author(s):  
E.S. Fraga ◽  
A. Kurkela ◽  
J. Schaffner-Bielich ◽  
A. Vuorinen
Keyword(s):  
Equation Of State ◽  
Compact Stars

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.

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