$R^2$引力中多角体白矮星的最大质量和理论限制
Maximal Masses of White Dwarfs for Polytropes in $R^2$ Gravity and Theoretical Constraints
摘要：
我们研究了白矮星在$f(R)$引力中的拉塞卡极限，用一个简单的多方状态方程描述恒星物质。我们使用最流行的$f(R)$引力模型，即$f(R)=R+αR^2$引力模型，用$p=Kρ^{1+1/n}$形式的多方状态方程计算了不同$n$参数值下的恒星构型参数。为了简化我们的分析，我们使用等价的爱因斯坦框架形式的$R^2$ -引力，这基本上是一个标量张量理论与众所周知的潜在的标量场。在这种描述中，人们可以使用简单的近似标量场$ϕ$只留下它的潜在的长期。我们的分析表明，对于非相对论的情况下与$n=3/2$，$R^2$ -重力和广义相对论之间的差异可以出现只有当参数$R^2$长期$α$，采取接近最大限度的值来自二进制脉冲星数据，即$α_{max}=5\times 10^{15}$厘米$^2$。因此，对低质量白矮星的研究很难对参数$α$给出限制。对于相对论性多面体与$n=3$，我们发现，在原则上可以改变更小的$α$值的Ekrasekhar限制。计算的主要结论是存在大质量$\sim 1.33 M_{\odot}$的白矮星，这对$R^2$引力模型的参数$α$有更严格的限制.具体而言，我们对$R^2$模型的参数$α$的估计是$α\sim 10^{13}$ cm $^2$。
英文摘要：
We examine the Chandrasekhar limit for white dwarfs in $f(R)$ gravity, with a simple polytropic equation of state describing stellar matter. We use the most popular $f(R)$ gravity model, namely the $f(R)=R+αR^2$ gravity, and calculate the parameters of the stellar configurations with polytropic equation of state of the form $p=Kρ^{1+1/n}$ for various values of the parameter $n$. In order to simplify our analysis we use the equivalent Einstein frame form of $R^2$-gravity which is basically a scalar-tensor theory with well-known potential for the scalar field. In this description one can use simple approximations for the scalar field $ϕ$ leaving only the potential term for it. Our analysis indicates that for the non-relativistic case with $n=3/2$, discrepancies between the $R^2$-gravity and General Relativity can appear only when the parameter $α$ of the $R^2$ term, takes values close to maximal limit derived from the binary pulsar data namely $α_{max}=5\times 10^{15}$ cm$^2$. Thus, the study of low-mass white dwarfs can hardly give restrictions on the parameter $α$. For relativistic polytropes with $n=3$ we found that Chandrasekhar limit can in principle change for smaller $α$ values. The main conclusion from our calculations is the existence of white dwarfs with large masses $\sim 1.33 M_{\odot}$, which can impose more strict limits on the parameter $α$ for the $R^2$ gravity model. Specifically, our estimations on the parameter $α$ of the $R^2$ model is $α\sim 10^{13}$ cm$^2$.
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