Rastall引力中的致密星：流体静力学平衡与径向脉动
Compact stars in Rastall gravity: hydrostatic equilibrium and radial pulsations
AI总结：
在Rastall引力中推导修正TOV方程与径向振荡方程，数值分析两种物态方程下致密星的稳定性，发现强子星在最大质量处失稳，而夸克星在负β值下可保持稳定，并证实结合能极小点对应基模频率为零。
摘要：
在Rastall引力框架下，我们研究了致密星的流体静力学平衡及其对径向脉动的动力学稳定性，其中自由参数$β$衡量了对广义相对论（GR）的偏离。我们推导了修正的Tolman-Oppenheimer-Volkoff（TOV）方程以及控制绝热径向振荡的Sturm-Liouville微分方程。通过数值求解这些方程，我们获得了两种真实状态方程下致密星的性质。对于强子物质，基模频率$ω_0$在对应于最大引力质量的临界中心能量密度附近变得不稳定。然而，对于夸克物质，需要较大的$\vertβ\vert$值才能在质量-半径图中观察到显著变化，当$β$为负值时，在最大质量构型之后仍存在稳定的恒星。通过独立分析，我们的结果表明，当将结合能作为固有质量的函数绘制时，尖点的出现可作为指示不稳定性发生的判据。具体而言，我们发现结合能最小处的中心密度值精确对应于$ω_0^2 =0$。
英文摘要：
Within the context of Rastall gravity, we investigate the hydrostatic equilibrium and dynamical stability against radial pulsations of compact stars, where a free parameter $β$ measures the deviations from General Relativity (GR). We derive both the modified Tolman-Oppenheimer-Volkoff (TOV) equations and the Sturm-Liouville differential equation governing the adiabatic radial oscillations. Such equations are solved numerically in order to obtain the compact-star properties for two realistic equations of state (EoSs). For hadronic matter, the fundamental mode frequency $ω_0$ becomes unstable almost at the critical central energy density corresponding to the maximum gravitational mass. However, for quark matter, where larger values of $\vertβ\vert$ are required to observe appreciable changes in the mass-radius diagram, there exist stable stars after the maximum-mass configuration for negative values of $β$. Using an independent analysis, our results reveal that the emergence of a cusp can be used as a criterion to indicate the onset of instability when the binding energy is plotted as a function of the proper mass. Specifically, we find that the central-density value where the binding energy is a minimum corresponds precisely to $ω_0^2 =0$.
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