$\mathscr{F}(Q)$ 引力中 Buchdahl 模型的最一般各向同性带电流体解
Most general isotropic charged fluid solution for Buchdahl model in $\mathscr{F}(Q)$ gravity
AI总结：
本研究首次在 $\mathscr{F}(Q)$ 引力框架下通过两步法求解 Buchdahl 模型的最一般各向同性带电流体解，验证其物理可行性并预测致密星最大质量极限。
摘要：
在本研究中，我们首次在 $\mathscr{F}(Q)$ 引力框架下，通过两步法研究了 Buchdahl 模型的最一般各向同性带电流体解。在此背景下，使用形式为 $\mathscr{F}(Q)=ζ_1 Q+ζ_2$ 的线性函数和特定变换，采用 Buchdahl 设定：$ e^{Υ(r)}=\frac{μ(1+λr^2)}{μ+λr^2}$ 来求解 Einstein-Maxwell 方程（EMEs），其中 $ζ_1$、$ζ_2$、$λ$ 和 $μ$ 为常数参数。将 Schwarzschild de Sitter (AdS) 外部解与内部解在边界处连接以确定常数参数。需要强调的是，对于给定的变换，Buchdahl 设定仅在电荷背景下提供数学上可行的解，此时压力和密度在中心处最大，并在 $0<μ<1$ 时向边界单调递减。我们考虑了质量 $M=(1.3\pm 0.2)M_{\odot}$、半径 $=12.02^{+0.55}_{-0.55}$ km 的致密星 EX01785-248 进行图形分析。通过考察能量条件、因果性、流体静力学平衡、压力-密度比等必要物理性质，评估了该模型在 $\mathscr{F}(Q)$ 背景下的物理可接受性。此外，我们预测了不同参数值下各类致密天体的最大质量极限及质量-半径关系。我们的解获得的最大质量范围为 (1.927 - 2.321) $M_\odot$。可以观察到，当 $\mathscr{F}(Q)$ 引力的耦合参数 $ζ_1$ 较小时，我们的解会产生大质量恒星。本研究为致密天体物理客体的形成提供了新见解和现实意义。
英文摘要：
In this work, we investigated a most general isotropic charged fluid solution for the Buchdahl model via a two-step method in $\mathscr{F}(Q)$-gravity framework for the first time. In this context, a linear function of the form $\mathscr{F}(Q)=ζ_1 Q+ζ_2$ and a particular transformation is used to solve the Einstein-Maxwell Equations (EMEs) employing the Buchdahl ansatz: $ e^{Υ(r)}=\frac{μ(1+λr^2)}{μ+λr^2}$, where $ζ_1$, $ζ_2$, $λ$ and $μ$ are constant parameters. The Schwarzschild de Sitter~(AdS) exterior solution is joined to the interior solution at the boundary to determine the constant parameters. It should be emphasized that, for a given transformation, the Buchdahl ansatz only offers a mathematically feasible solution in the context of electric charge, where pressure and density are maximum at the center and decrease monotonically towards the boundary when $0<μ<1$. We taken into account the compact star EX01785-248 with $M=(1.3\pm 0.2)M_{\odot}$; Radius $=12.02^{+0.55}_{-0.55}$~km for graphical analysis. The physical acceptability of the model in the context of $\mathscr{F}(Q)$ has been evaluated by looking at the necessary physical properties, including energy conditions, causality, hydrostatic equilibrium, pressure-density ratio, etc. Additionally, we predicted the maximum mass limit of different compact objects for various parameter values along with the mass-radius relation. The maximum masses range (1.927 - 2.321)~$M_\odot$ are obtained for our solution. It can be observed that when the coupling parameter $ζ_1$ for $\mathscr{F}(Q)$ gravity is smaller, then our solution yields massive stars. The present investigation provides novel insights and realistic implications regarding the formation of compact astrophysical objects.
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