Black hole perturbation theory is a useful approach to study interactions between black holes and fundamental fields. A particular class of black hole solutions arising out of modification of Einstein’s general theory of relativity are regular black holes (RBHs) which can be constructed using a nonlinear electrodynamic Lagrangian. Because of their importance, we are interested in studying the behavior of three kinds of such RBHs under perturbations generated by an external field. Indeed, we investigate the quasinormal modes (QNMs) of a massive scalar field propagating near the RBHs which is non-minimally coupled to the Ricci scalar-tensor of background geometry. We will attempt to find the low-lying quasinormal frequencies of the perturbations by using WKB approximation. We shall also study the relationship between the QNMs and some characteristic properties of black holes such as grey-body factors, area quantization, and shadow radius.

黑洞微扰理论是研究黑洞与基本场之间相互作用的有用方法。由于爱因斯坦广义相对论的修正而产生的一类特殊的黑洞解是规则黑洞 (RBH)，它可以使用非线性电动拉格朗日量来构建。由于它们的重要性，我们有兴趣研究三种此类 RBH 在外场产生的扰动下的行为。事实上，我们研究了在 RBH 附近传播的大规模标量场的准正规模式 (QNM)，它与背景几何的 Ricci 标量张量非最小耦合。我们将尝试通过使用 WKB 近似来找到扰动的低位准正规频率。