标题： Rastall引力中的致密星体：流体静力平衡与径向脉动 显示英文标题

标题： Compact stars in Rastall gravity: hydrostatic equilibrium and radial pulsations

摘要： 在Rastall引力的背景下，我们研究了致密星体的流体静力平衡和径向脉动的动力学稳定性，其中自由参数$\beta$衡量与广义相对论（GR）的偏差。 我们推导了修改后的 Tolman-Oppenheimer-Volkoff（TOV）方程以及描述绝热径向振荡的Sturm-Liouville微分方程。 这些方程通过数值方法求解，以获得两种现实状态方程（EoSs）下的致密星体特性。 对于强子物质，基频频率$\omega_0$几乎在对应最大引力质量的临界中心能量密度处变得不稳定。 然而，对于夸克物质，需要较大的$\vert\beta\vert$值才能在质量-半径图中观察到显著变化，在$\beta$为负值时，最大质量构型之后仍存在稳定星体。 通过独立分析，我们的结果表明，当结合能作为固有质量的函数绘制时，尖点的出现可以作为不稳定开始的判据。 具体而言，我们发现结合能最小的中心密度值正好对应$\omega_0^2 =0$。 显示英文摘要

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 $\beta$ 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 $\omega_0$ becomes unstable almost at the critical central energy density corresponding to the maximum gravitational mass. However, for quark matter, where larger values of $\vert\beta\vert$ are required to observe appreciable changes in the mass-radius diagram, there exist stable stars after the maximum-mass configuration for negative values of $\beta$. 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 $\omega_0^2 =0$.