scholarly journals Equation-of-state of neutron stars with junction conditions in the Starobinsky model

2017 ◽  
Vol 27 (01) ◽  
pp. 1750186 ◽  
Author(s):  
Wei-Xiang Feng ◽  
Chao-Qiang Geng ◽  
W. F. Kao ◽  
Ling-Wei Luo
Keyword(s):  
Equation Of State ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Neutron Stars ◽  
Junction Conditions ◽  
Coupled Differential Equations ◽  
Starobinsky Model ◽  
Structure Equations ◽  
Text Model ◽  
Minimal Mass

We study the Starobinsky or [Formula: see text] model of [Formula: see text] for neutron stars with the structure equations represented by the coupled differential equations and the polytropic type of the matter equation-of-state (EoS). The junction conditions of [Formula: see text] gravity are used as the boundary conditions to match the Schwarzchild solution at the surface of the star. Based on these the conditions, we demonstrate that the coupled differential equations can be solved directly. In particular, from the dimensionless EoS [Formula: see text] with [Formula: see text] and [Formula: see text] and the constraint of [Formula: see text], we obtain the minimal mass of the NS to be around 1.44 [Formula: see text]. In addition, if [Formula: see text] is larger than 5.0, the mass and radius of the NS would be smaller.

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.

scholarly journals QUARK–DIQUARK EQUATIONS OF STATE MODELS: THE ROLE OF INTERACTIONS

2003 ◽  
Vol 12 (03) ◽  
pp. 519-526 ◽  
Author(s):  
J. E. HORVATH ◽  
G. LUGONES ◽  
J. A. DE FREITAS PACHECO
Keyword(s):  
Equation Of State ◽  
Boundary Conditions ◽  
Neutron Stars ◽  
Hard Sphere ◽  
Degrees Of Freedom ◽  
Equations Of State ◽  
Compact Star ◽  
Star Models ◽  
State Models

Recent observational data suggests a high compacticity (the quotient M/R) of some "neutron" stars. Motivated by these works we revisit models based on quark–diquark degrees of freedom and address the question of whether that matter is stable against diquark disassembling and hadronization within the different models. We find that equations of state modeled as effective λϕ4 theories do not generally produce stable self-bound matter and are not suitable for constructing very compact star models, that is the matter would decay into neutron matter. We also discuss some insights obtained by including hard sphere terms in the equation of state to model repulsive interactions. We finally compare the resulting equations of state with previous models and emphasize the role of the boundary conditions at the surface of compact self-bound stars, features of a possible normal crust of the latter and related topics.

scholarly journals Short introduction to the physics of neutron stars

2020 ◽  
Vol 227 ◽  
pp. 01018 ◽  
Author(s):  
Isaac Vidaña
Keyword(s):  
Equation Of State ◽  
Neutron Stars ◽  
Short Introduction ◽  
Different Types ◽  
Structure Equations ◽  
Composition Structure ◽  
The Many

Here we briefly review several aspects of the physics of neutron stars.In particular, we shortly describe the different types of telescopes employed in their observation, the many astrophysical manifestations of these objects and the measurement of observables such as their masses and radii. A brief summary of their composition, structure equations and equation of state is also presented.

scholarly journals Neutron stars in Palatini $$R+\alpha R^2$$ and $$R+\alpha R^2+\beta Q$$ theories

2021 ◽  
Vol 81 (10) ◽  
Author(s):  
Georg Herzog ◽  
Hèlios Sanchis-Alepuz
Keyword(s):  
General Relativity ◽  
Equation Of State ◽  
Neutron Stars ◽  
Equations Of State ◽  
Stellar Structure ◽  
Modified Theories Of Gravity ◽  
State Uncertainty ◽  
Structure Equations ◽  
Theories Of Gravity

AbstractWe study solutions of the stellar structure equations for spherically symmetric objects in modified theories of gravity, where the Einstein-Hilbert Lagrangian is replaced by $$f(R)=R+\alpha R^2$$ f ( R ) = R + α R 2 and $$f(R,Q)=R+\alpha R^2+\beta Q$$ f ( R , Q ) = R + α R 2 + β Q , with R being the Ricci scalar curvature, $$Q=R_{\mu \nu }R^{\mu \nu }$$ Q = R μ ν R μ ν and $$R_{\mu \nu }$$ R μ ν the Ricci tensor. We work in the Palatini formalism, where the metric and the connection are assumed to be independent dynamical variables. We focus on stellar solutions in the mass-radius region associated to neutron stars. We illustrate the potential impact of the $$R^2$$ R 2 and Q terms by studying a range of viable values of $$\alpha $$ α and $$\beta $$ β . Similarly, we use different equations of state (SLy, FPS, HS(DD2) and HS(TMA)) as a simple way to account for the equation of state uncertainty. Our results show that for certain combinations of the $$\alpha $$ α and $$\beta $$ β parameters and equation of state, the effect of modifications of general relativity on the properties of stars is sizeable. Therefore, with increasing accuracy in the determination of the equation of state for neutron stars, astrophysical observations may serve as discriminators of modifications of General Relativity.

scholarly journals Stellar Structure Models of Deformed Neutron Stars

2017 ◽  
Vol 45 ◽  
pp. 1760029 ◽  
Author(s):  
Omair Zubairi ◽  
David Wigley ◽  
Fridolin Weber
Keyword(s):  
General Relativity ◽  
Equation Of State ◽  
Neutron Stars ◽  
Two Dimensions ◽  
Stellar Structure ◽  
Anisotropic Model ◽  
Pressure Profiles ◽  
Spherical Models ◽  
Structure Equations ◽  
Stellar Properties

Traditional stellar structure models of non-rotating neutron stars work under the assumption that these stars are perfect spheres. This assumption of perfect spherical symmetry is not correct if the matter inside neutron stars is described by an anisotropic model for the equation of state. Certain classes of neutron stars such as Magnetars and neutron stars which contain color-superconducting quark matter cores are expected to be deformed making them oblong spheroids. In this work, we investigate the stellar structure of these deformed neutron stars by deriving stellar structure equations in the framework of general relativity. Using a non-isotropic equation of state model, we solve these structure equations numerically in two dimensions. We calculate stellar properties such as masses and radii along with pressure profiles and investigate changes from standard spherical models.

Flexural Vibration of Pretwisted Tapered Cantilever Blades

1972 ◽  
Vol 94 (1) ◽  
pp. 343-346 ◽  
Author(s):  
J. S. Rao
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Equations Of Motion ◽  
Flexural Vibration ◽  
Uniform Beam ◽  
Coupled Differential Equations ◽  
Experimental Values

The Ritz-Galerkin process is used to solve the two coupled differential equations of motion of a pretwisted tapered cantilever blade vibrating in flexure. A five-term solution for each y and x deflection satisfying the boundary conditions is found to give accurate values for the first three modes of a uniform beam. Using these five-term solutions the first five coupled frequencies of pretwisted tapered cantilever blades are determined and compared with experimental values of some typical blades. The theoretical values of frequencies obtained are shown to be in favorable agreement with the experimental values.

Sign in / Sign up

Export Citation Format

Share Document