满足Karmarkar条件的各向异性球在$f(\mathscr{R},\mathscr{G})$引力场中的物理可行解
Physically viable solutions of anisotropic spheres in $f(\mathscr{R},\mathscr{G})$ gravity satisfying the Karmarkar condition
摘要：
本文讨论了在$f(\mathscr{R},\mathscr{G})$引力下的致密星，其中$\mathscr{R}$和$\mathscr{G}$分别表示Ricci标量和Gauss-Bonnet不变量.为了达到这一目的，我们考虑球对称时空各向异性流体分布。特别地，Karmarkar条件被用来探索紧致星解。此外，我们还选取了两个特定的致密星模型，即LMC X-4（质量=1.29 $M/M_{\odot}$ &半径=9.711 km）和EXO 1785-248（质量=1.30 $M/M_{\odot}$ &半径=8.849 km）。我们通过采用Karmarkar条件和Lake [Phys. Rev. D 67，104015（2003）]文献中已经报道的特定模型，建立了$f(\mathscr{R},\mathscr{G})$重力场方程。我们进一步考虑Schwarzschild几何的匹配条件的边界。这里需要强调的是，我们通过施加匹配条件来计算所有相关参数的值。我们提供了详细的图形分析来讨论参数的物理可接受性，即，能量密度、压力、各向异性和梯度。我们还从能量条件、物态方程、广义Tolman-Oppenheimer-Schmidoff方程、因果关系条件和绝热指数等方面研究了致密星的稳定性。对于目前的分析，我们预测了一些数值的表格形式的中心引力度规函数，中心密度和中心压力分量。我们还计算了比率$p_{rc}/ ρ_{c}$以检验Zeldovich条件的有效性。最后，我们发现对于所讨论的致密星模型，我们获得的解在物理上是可行的，并且在$f(\mathscr{R},\mathscr{G})$修改的引力中具有良好的性质。
英文摘要：
This paper is devoted to discuss compact stars in $f(\mathscr{R},\mathscr{G})$ gravity, where $\mathscr{R}$ and $\mathscr{G}$ denote the Ricci scalar and Gauss-Bonnet invariant respectively. To meet this aim, we consider spherically symmetric space-time with anisotropic fluid distribution. In particular, the Karmarkar condition is used to explore the compact star solutions. Further, we choose two specific model of compact stars namely LMC X-4 (mass =1.29$M/M_{\odot}$ \& radii=9.711 km) and EXO 1785-248 (mass =1.30$M/M_{\odot}$ \& radii=8.849 km). We develop the field equations for $f(\mathscr{R},\mathscr{G})$ gravity by employing the Karmarkar condition with a specific model already reported in literature by Lake [Phys. Rev. D 67, 104015 (2003)]. We further consider the Schwarzschild geometry for matching conditions at the boundary. It is important to mention here that we calculate the values of all the involved parameter by imposing the matching condition. We have provided a detailed graphical analysis to discuss the physical acceptability of parameters, i.e., energy density, pressure, anisotropy, and gradients. We have also examined the stability of compacts stars by exploring the energy conditions, equation of state, generalized Tolman-Oppenheimer-Volkoff equation, causality condition, and adiabatic index. For present analysis, we predict some numerical values in tabular form for central gravitational metric functions, central density and central pressures components. We have also calculated the ratio $p_{rc}/ ρ_{c}$ to check the validity of Zeldovich's condition. Conclusively, it is found that our obtained solutions are physically viable with well-behaved nature in $f(\mathscr{R},\mathscr{G})$ modified gravity for the compact star models under discussion.
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