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 \(\omega _0^2 =0\).

在拉斯塔尔引力的背景下，我们研究了致密星径向脉动的流体静力平衡和动力学稳定性，其中自由参数\(\beta \)测量与广义相对论 (GR) 的偏差。我们推导了修正的托尔曼-奥本海默-沃尔科夫（TOV）方程和控制绝热径向振荡的斯特姆-刘维尔微分方程。对此类方程进行数值求解，以获得两个现实状态方程 (EoS) 的致密星特性。对于强子物质，基模频率\(\omega _0\)几乎在与最大引力质量对应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\(\vert \beta \vert \)值才能观察质量半径图的明显变化，在负值\(\测试版\）。通过独立分析，我们的结果表明，当将结合能绘制为适当质量的函数时，尖点的出现可以用作指示不稳定开始的标准。具体来说，我们发现结合能最小的中心密度值恰好对应于\(\omega _0^2 =0\)。