发表机构
Faculty of Science, Kunming University of Science and Technology（昆明理工大学理学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文在STVG框架下研究修正引力中Reissner-Nordström黑洞的准正则模，通过高阶WKB和Padé近似及有限差分法计算，发现MOG参数和电荷增大降低阻尼率，为黑洞光谱学检验修正引力提供理论参考。
AI 中文摘要
在标量-张量-矢量引力（STVG）框架下，本文研究了无质量标量、电磁和引力扰动下Reissner-Nordström修正引力（MOG）黑洞的准正则模和时域演化。通过将3阶至6阶WKB方法扩展并与Padé近似结合至13阶来计算准正则频率，同时使用基于光锥坐标的有限差分方法获得完整的时域波形。结果表明，增加MOG参数$\alpha$会提高黑洞的有效质量，导致阻尼率$|\omega_I|$减小，振铃衰减变慢。电荷$Q$的增加产生类似效应，在近极端极限下阻尼趋近于零。对于三种类型扰动的振铃衰减时间，引力场持续时间最长，电磁场居中，标量场最短。时域波形中观察到的振荡和衰减与频域结果定性一致，晚期尾巴的幂律指数与渐近平直时空一致。本研究为利用黑洞光谱学检验修正引力理论提供了系统的理论参考。
英文摘要
In the framework of Scalar-Tensor-Vector Gravity (STVG), this paper investigates the quasinormal modes and time-domain evolution of Reissner-Nordström Modified Gravity (MOG) black holes under massless scalar, electromagnetic, and gravitational perturbations. Quasinormal frequencies are calculated by extending the 3rd- to 6th-order WKB method and combining it with Padé approximation to the 13th order, while complete time-domain waveforms are obtained using a finite-difference method based on light-cone coordinates. The results indicate that increasing the MOG parameter $α$ raises the effective mass of the black holes, leading to a decrease in the damping rate $|ω_I|$ and a slower ringdown decay. An increase in charge $Q$ produces a similar effect, with the damping approaching zero in the near-extremal limit. Regarding the ringdown decay times for the three types of perturbations, the gravitational field has the longest duration, the electromagnetic field is intermediate, and the scalar field is the shortest. The oscillations and decay observed in the time-domain waveforms are qualitatively consistent with the frequency-domain results, and the power-law exponent governing the late-time tail aligns with that of asymptotically flat spacetimes. This study provides a systematic theoretical reference for testing modified gravity theories using black hole spectroscopy.
Comments14 pages, 9 figures, 10 tables
