In this work, the Dirac equation is studied in the [Formula: see text] Lifshitz black hole ([Formula: see text]LBH) spacetime. The set of equations representing the Dirac equation in the Newman–Penrose (NP) formalism is decoupled into a radial set and an angular set. The separation constant is obtained with the aid of the spin weighted spheroidal harmonics. The radial set of equations, which are independent of mass, is reduced to Zerilli equations (ZEs) with their associated potentials. In the near horizon (NH) region, these equations are solved in terms of the Bessel functions of the first and second kinds arising from the fermionic perturbation on the background geometry. For computing the boxed quasinormal modes (BQNMs) instead of the ordinary quasinormal modes (QNMs), we first impose the purely ingoing wave condition at the event horizon. Then, Dirichlet boundary condition (DBC) and Newmann boundary condition (NBC) are applied in order to get the resonance conditions. For solving the resonance conditions, we follow the Hod’s iteration method. Finally, Maggiore’s method (MM) is employed to derive the entropy/area spectra of the [Formula: see text]LBH which are shown to be equidistant.

中文翻译：

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z = 0 Lifshitz 黑洞周围的费米子云

在这项工作中，狄拉克方程在 [公式：见文本] Lifshitz 黑洞（[公式：见文本]LBH）时空中进行了研究。表示 Newman-Penrose (NP) 形式中的狄拉克方程的方程组被解耦为径向集和角集。借助自旋加权球谐函数获得分离常数。与质量无关的径向方程组被简化为具有相关势的 Zerilli 方程 (ZE)。在近视界 (NH) 区域，这些方程根据由背景几何上的费米子扰动产生的第一类和第二类贝塞尔函数来求解。为了计算盒装准正常模式（BQNMs）而不是普通准正常模式（QNMs），我们首先在事件视界施加纯入波条件。然后，应用狄利克雷边界条件 (DBC) 和纽曼边界条件 (NBC) 以获得共振条件。为了解决共振条件，我们遵循 Hod 迭代法。最后，采用 Maggiore 方法 (MM) 推导出 [公式：见正文] LBH 的熵/面积谱，显示为等距。