We study the stability of static, spherically symmetric solutions of Rastall’s theory in the presence of a scalar field with respect to spherically symmetric perturbations. The analysis of perturbations shows that there arises an inconsistency in the sense that time-dependent perturbations do not exist in any order of perturbation theory, and we can conclude that these solutions are pertubatively stable (though nonperturbative time-dependent solutions are not excluded). Possible reasons for this inconsistency are discussed.

中文翻译：

---

拉斯特尔的重力理论：球对称解和稳定性问题

我们研究相对于球对称摄动的标量场存在下Rastall理论的静态球对称解的稳定性。扰动分析表明，从某种意义上说，在任何阶次的扰动理论中都不存在与时间有关的扰动，因此我们可以得出结论：这些解是扰动上稳定的（尽管不排除非扰动的与时间有关的解）。讨论了这种不一致的可能原因。