In this paper, we study the quasinormal modes of the massless Dirac field for charged black holes in Rastall gravity. The spherically symmetric black hole solutions in question are characterized by the presence of a power-Maxwell field, surrounded by the quintessence fluid. The calculations are carried out by employing the WKB approximations up to the 13th-order, as well as the matrix method. The temporal evolution of the quasinormal modes is investigated by using the finite difference method. Through numerical simulations, the properties of the quasinormal frequencies are analyzed, including those for the extremal black holes. Among others, we explore the case of a second type of extremal black holes regarding the Nariai solution, where the cosmical and event horizon coincide. The results obtained by the WKB approaches are found to be mostly consistent with those by the matrix method. It is observed that the magnitudes of both real and imaginary parts of the quasinormal frequencies increase with increasing [Formula: see text], the spin–orbit quantum number. Also, the roles of the parameters [Formula: see text] and [Formula: see text], associated with the electric charge and the equation of state of the quintessence field, respectively, are investigated regarding their effects on the quasinormal frequencies. The magnitude of the electric charge is found to sensitively affect the time scale of the first stage of quasinormal oscillations, after which the temporal oscillations become stabilized. It is demonstrated that the black hole solutions for Rastall gravity in asymptotically flat spacetimes are equivalent to those in Einstein gravity, featured by different asymptotical spacetime properties. As one of its possible consequences, we also investigate the behavior of the late-time tails of quasinormal models in the present model. It is found that the asymptotical behavior of the late-time tails of quasinormal modes in Rastall theory is governed by the asymptotical properties of the spacetimes of their counterparts in Einstein gravity.

中文翻译：

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拉斯托引力中幂-麦克斯韦带电黑洞的狄拉克准正常模式

在本文中，我们研究了拉斯托引力中带电黑洞的无质量狄拉克场的准正常模式。所讨论的球对称黑洞解决方案的特点是存在一个被精华流体包围的幂麦克斯韦场。通过使用高达 13 阶的 WKB 近似以及矩阵方法进行计算。使用有限差分法研究了准正态模式的时间演化。通过数值模拟，分析了准正常频率的特性，包括极值黑洞的特性。除其他外，我们探讨了关于 Nariai 解的第二种极端黑洞的情况，其中宇宙和事件视界重合。WKB 方法得到的结果与矩阵方法得到的结果基本一致。可以观察到，准正常频率的实部和虚部的幅度都随着自旋轨道量子数的增加[公式：见正文]而增加。此外，还研究了分别与典型场的电荷和状态方程相关的参数[公式：见正文]和[公式：见正文]的作用，了解它们对准正规频率的影响。发现电荷的大小敏感地影响准正常振荡的第一阶段的时间尺度，之后时间振荡变得稳定。证明了拉斯托引力在渐近平坦时空的黑洞解与爱因斯坦引力的黑洞解是等价的，具有不同的渐近时空性质。作为其可能的后果之一，我们还研究了当前模型中准常态模型的后期尾部的行为。研究发现，Rastall 理论中准正态模式后期尾的渐近行为受爱因斯坦引力中对应的时空渐近性质的支配。