We study the stability of relativistic stars in scalar-tensor theories with a nonminimal coupling of the form $F(\varphi )R$, where $F$ depends on a scalar field $\varphi$ and $R$ is the Ricci scalar. On a spherically symmetric and static background, we incorporate a perfect fluid minimally coupled to gravity as a form of the Schutz-Sorkin action. The odd-parity perturbation for the multipoles $l\ge 2$ is ghost-free under the condition $F(\varphi )>0$, with the speed of gravity equivalent to that of light. For even-parity perturbations with $l\ge 2$, there are three propagating degrees of freedom arising from the perfect-fluid, scalar-field, and gravity sectors. For $l=0,1$, the dynamical degrees of freedom reduce to two modes. We derive no-ghost conditions and the propagation speeds of these perturbations and apply them to concrete theories of hairy relativistic stars with $F(\varphi )>0$. As long as the perfect fluid satisfies a weak energy condition with a positive propagation speed squared $c_m^2$, there are neither ghost nor Laplacian instabilities for theories of spontaneous scalarization and Brans-Dicke (BD) theories with a BD parameter $\omega_{\rm BD}>-3/2$ (including $f(R)$ gravity). In these theories, provided $0

中文翻译：

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具有标量毛发的相对论恒星的稳定性

我们在标量张量理论中研究相对论恒星的稳定性，其形式为非最小耦合 $F（\varphi ）\mathrm{[R}$，在哪里 $F$ 取决于标量场 $\varphi$ 和 $\mathrm{[R}$是Ricci标量。在球形对称和静态背景下，我们引入了一种最小化与重力耦合的完美流体，作为Schutz-Sorkin动作的一种形式。多极的奇偶奇摄动$升\ge 2$ 在以下条件下无鬼影 $F（\varphi ）>0$，其重力速度等于光速。对于偶数奇偶摄动$升\ge 2$，由完美流体，标量场和重力扇区产生的三个传播自由度。对于$升=0，\mathrm{1个}$，动态自由度降低为两种模式。我们推导无鬼的条件和这些扰动的传播速度，并将其应用于具有毛细相对论的恒星的具体理论$F（\varphi ）>0$。只要理想流体满足弱能量条件，且传播速度为正数$C_{米}^2$，既没有鬼也不拉普拉斯不稳定用于与BD参数自发标量化和布兰斯-迪克（BD）的理论的理论$ \欧米加_ {\ RM BD}> - 3/2 $（包括$F（\mathrm{[R}）$重力）。在这些理论中，提供了$ 0