Starobinsky模型中具有结条件的中子星的物态方程
Equation of State of Neutron Stars with Junction Conditions in the Starobinsky Model
摘要：
本文研究了中子星的Starobinsky或$R^2$模型，其结构方程为耦合微分方程和\emph{polytropic}型物质状态方程。$f(R)$引力的连接条件被用作边界条件，以匹配在恒星表面的史瓦西解。在此基础上，证明了耦合微分方程组可以用\emph{directly}求解.特别地，从具有$\bar{k}\sim5.0$和$γ\sim0.75$的无量纲状态方程$\barρ = \bar{k}\, \bar{p}^{\,γ}$和$α\lesssim {1.47722}\times 10^{7}\, \text{m}^2$的约束，我们获得NS的\emph{minimal}质量为大约1.44 $M_{\odot}$。此外，如果$\bar{k}$大于5.0，NS的质量和半径将更小。
英文摘要：
We study the Starobinsky or $R^2$ model of $f(R)=R+αR^2$ 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 $\barρ = \bar{k}\, \bar{p}^{\,γ}$ with $\bar{k}\sim5.0$ and $γ\sim0.75$ and the constraint of $α\lesssim {1.47722}\times 10^{7}\, \text{m}^2$, 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.
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