发表机构
University of Cape Town; Botswana International University of Science and Technology; University of South Africa; University of Oslo（开普敦大学; 博茨瓦纳国际科学与技术大学; 南非大学; 奥斯陆大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文在 Bondi-Sachs 形式下研究 $f(R)$ 引力中 Schwarzschild 黑洞的标量场准正则模与准束缚态，通过连分式法和特征演化独立验证频率，并实现单半径双谱提取。
AI 中文摘要
我们直接在度规 $f(R)$ 引力的 Bondi-Sachs 形式中研究 Schwarzschild 黑洞的标量场准正则模和准束缚态，将频域分析与特征时间演化相结合。从线性化的特征方程出发，我们得到有质量标量主方程，并表明张量主方程与广义相对论中的形式相同。对于此处考虑的解析模型，线性标量谱仅通过无量纲组合 $\mu M$ 依赖于 $f(R)$ 理论。我们使用 Leaver 的连分式方法计算准正则和准束缚谱分支，并将其与独立的文献基准进行比较。为补充频域分析，我们使用四阶收敛特征格式演化标量场扰动方程。将矩阵束稳定性扫描应用于所得波形，我们在测量的提取稳定性尺度内独立恢复了与连分式结果一致的基本准正则频率。最后，对于选定的有限质量情形，我们展示了在单个提取半径处从同一波形的不同时间窗口提取基本准正则模和准束缚态的振荡频率和阻尼率，而无需在有限外边界处施加任一谱分支。
英文摘要
We study scalaron quasinormal modes and quasi-bound states of Schwarzschild black holes directly within the Bondi-Sachs formulation of metric $f(R)$ gravity, combining frequency-domain analyses with characteristic time evolution. Starting from the linearised characteristic equations, we obtain the massive scalar master equation and show that the tensor master equation takes the same form as in general relativity. For the analytic models considered here, the linear scalar spectra depend on the $f(R)$ theory only through the dimensionless combination $μM$. We compute both quasinormal and quasi-bound spectral branches using Leaver's continued-fraction method and compare them with independent literature benchmarks. To complement the frequency domain analysis, we evolve the scalaron perturbation equations using a fourth order convergent characteristic scheme. Applying matrix-pencil stability scans to the resulting waveforms, we independently recover fundamental quasinormal frequencies consistent with the continued-fraction results within the measured extraction-stability scales. Finally, for a selected finite-mass case, we demonstrate the extraction of both oscillation frequencies and damping rates of the fundamental quasinormal mode and quasi-bound state from separate time windows of the same waveform at one extraction radius, without imposing either spectral branch at the finite outer boundary.
Comments41 pages, 8 figures, 9 tables
