arXiv 2002.081602020-02-15gr-qc

在$f(R,T)-$引力中探索致密星的物理性质：一种嵌入方法

Exploring physical properties of compact stars in $f(R,T)-$gravity: An embedding approach

Ksh. Newton Singh, Abdelghani Errehymy, Farook Rahaman, Mohammed Daoud

备注：: 26 Pages, 14 figures

摘要：

精确求解$f(R,T)$引力场方程是一项困难的工作。为此，许多作者采用了不同的方法，如假设两个度量函数，状态方程（EoS）和度量函数等，但是，这样的方法可能并不总是导致良好的解决方案，从而拒绝的解决方案可能会发生后，完成计算。事实上，最近的作品嵌入类一方法表明，到达良好的收敛的解决方案的机会是非常高的，从而启发我们使用它。在类一的方法，我们必须ananimation的度量潜力之一，另一个可以从Karmarkar条件获得。在本文中，我们提出了新的一类解决方案，这是良好的表现在所有的物理观点。我们通过调节$f(R,T)-$耦合参数$χ$分析了解的性质，发现解导致$χ=-1$的EoS比$χ=1$更硬。这是因为对于较小的$χ$值，声速越大，$M-R$曲线中的$M_{max}$越高，并且EoS参数$ω$越大。该解满足因果关系条件、能量条件、在径向扰动下的稳定性和静态性（静态稳定性判据）以及平衡状态下的稳定性和静态性（修正的TOV方程）。由该解得到的$M-R$图与PSR J1614-2230、船帆座X-1、天鹰座X-3和SAX J1808.4-3658等致密星的观测值吻合得很好。因此，对于不同的$χ$值，我们已经从$M-I$曲线预测了相应的半径和它们各自的惯性矩。

英文摘要：

Solving field equations exactly in $f(R,T)$ gravity is one of the difficult task. To do so, many authors have adopted different methods such as assuming both the metric functions, an equation of state (EoS) and a metric function etc. However, such methods may not always lead to well-behaved solutions and thereby rejection of the solutions may happen after complete calculations. Indeed, very recent works on embedding class one methods suggested that the chances of arriving at the well behaved-solution is very high thereby inspired us to used it. In class one approach, we have to ansatz one of the metric potentials and the other can be obtain from the Karmarkar condition. In this paper, we are proposing new class one solution which is well-behaved in all physical points of view. We have analyzed the nature of the solution by tuning the $f(R,T)-$coupling parameter $χ$ and found that the solution results into stiffer EoS for $χ=-1$ than $χ=1$. This is because for lesser values of $χ$, velocity of sound is more, higher $M_{max}$ in $M-R$ curve and the EoS parameter $ω$ is larger. The solution satisfy the causality condition, energy conditions, stable and static under radial perturbations (static stability criterion) and in equilibrium (modified TOV-equation). The resulting $M-R$ diagram from this solution is well fitted with observed values of few compact stars such as PSR J1614-2230, Vela X-1, Cen X-3 and SAX J1808.4-3658. Therefore, for different values of $χ$, we have predicted the corresponding radii and their respective moment of inertia from the $M-I$ curve.

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英文摘要：

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