Equation of State of Neutron Stars with Junction Conditions in the Starobinsky Model

Abstract

We study the Starobinsky or $R^2$ model of $f(R)=R+\alpha R^2$ for neutron stars with the structure equations represented by the coupled differential equations and the \emph{polytropic} type of the matter equation of state. The junction conditions of $f(R)$ gravity are used as the boundary conditions to match the Schwarschild solution at the surface of the star. Based on these the conditions, we demonstrate that the coupled differential equations can be solved \emph{directly}. In particular, from the dimensionless equation of state $\bar{\rho }=\bar{k}{\bar{p}}^{\gamma }$ with $\bar{k}\sim 5.0$ and $\gamma \sim 0.75$ and the constraint of $\alpha \lesssim 1.47722\times 10^7{\text{m}}^2$, we obtain the \emph{minimal} mass of the NS to be around 1.44 $M_{\odot }$. In addition, if $\bar{k}$ is larger than 5.0, the mass and radius of the NS would be smaller.

18 pages, 3 figures, revised version accepted by Int. J. Mod. Phys. D

References in corpus (58)

• Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant
• Measurements of Omega and Lambda from 42 High-Redshift Supernovae
• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Determination of Cosmological Parameters
• Wilkinson Microwave Anisotropy Probe (WMAP) Three Year Results: Implications for Cosmology
• Dynamics of dark energy
• Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation
• The Cosmological Constant and Dark Energy
• Detection of the Baryon Acoustic Peak in the Large-Scale Correlation Function of SDSS Luminous Red Galaxies
• f(R) Theories Of Gravity
• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• Cosmological parameters from SDSS and WMAP
• f(R) theories
• Cosmological Constant - the Weight of the Vacuum
• The Case for a Positive Cosmological Lambda-term
• Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution
• The Cosmological Constant
• Models of f(R) Cosmic Acceleration that Evade Solar-System Tests
• Disappearing cosmological constant in f(R) gravity
• Cosmological parameter analysis including SDSS Ly-alpha forest and galaxy bias: constraints on the primordial spectrum of fluctuations, neutrino mass, and dark energy
• The Nuclear Equation of State and Neutron Star Masses
• Class of viable modified $f(R)$ gravities describing inflation and the onset of accelerated expansion
• Equation of state and neutron star properties constrained by nuclear physics and observation
• Unifying inflation with LambdaCDM epoch in modified f(R) gravity consistent with Solar System tests
• Observational signatures of f(R) dark energy models that satisfy cosmological and local gravity constraints
• Constraints on neutron star radii based on chiral effective field theory interactions
• Hydrostatic equilibrium and stellar structure in f(R)-gravity
• The Mass-Radius relation for Neutron Stars in $f(R)$ gravity
• Phantom scalar dark energy as modified gravity: understanding the origin of the Big Rip singularity
• The future evolution and finite-time singularities in $F(R)$-gravity unifying the inflation and cosmic acceleration
• Constraints on Perturbative f(R) Gravity via Neutron Stars
• A Singularity Problem with f(R) Dark Energy
• Neutron Stars in f(R) Gravity with Perturbative Constraints
• Relativistic stars in f(R) gravity, and absence thereof
• Nonperturbative models of quark stars in $f(R)$ gravity
• Junction Conditions in f(R) Theories of Gravity
• Junction conditions for F(R)-gravity and their consequences
• Slowly rotating neutron and strange stars in $R^2$ gravity
• Non-perturbative and self-consistent models of neutron stars in R-squared gravity
• Neutron Matter from Low to High Density
• A no-go theorem for polytropic spheres in Palatini f(R) gravity
• Neutron stars in Starobinsky model
• The existence of relativistic stars in f(R) gravity
• Relativistic stars in f(R) and scalar-tensor theories
• Modified TOV in gravity's rainbow: properties of neutron stars and dynamical stability conditions
• Structure of neutron stars in R-squared gravity
• Rapidly rotating neutron stars in $R$-squared gravity
• Modified gravity with logarithmic curvature corrections and the structure of relativistic stars
• Robust approach to f(R) gravity
• Buchdahl-Bondi limit in modified gravity: Packing extra effective mass in relativistic compact stars
• Neutron stars in a perturbative $f(R)$ gravity model with strong magnetic fields
• On the compactness of neutron stars
• Neutron stars in generalized f(R) gravity
• Dilatonic Equation of Hydrostatic Equilibrium and Neutron Star Structure
• Jebsen-Birkhoff theorem and its stability in f(R) gravity
• Neutron stars in Einstein-$\Lambda$ gravity: the cosmological constant effects
• Quantum vacuum effects as generalized f(R) gravity. Application to stars
• Moment of inertia of neutron star crust in alternative and modified theories of gravity
• Order-of-magnitude physics of neutron stars

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