发表机构
Universitá di Napoli “Federico II”; Istituto Nazionale di Fisica Nucleare, Sezione di Napoli; University of Tübingen; Scuola Superiore Meridionale（那不勒斯费德里科二世大学; 意大利国家核物理研究所，那不勒斯分部; 蒂宾根大学; 南方高等学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究通过时域实现参数化超越特克尔什基框架，用高斯波包做散射实验，提供微扰线性演化。对比频域结果，分析模式精度、系数及变形参数对铃宕和晚期行为的影响，为测试广义相对论偏差提供互补灵活框架。
AI 中文摘要
对广义相对论的修改会显著改变黑洞的微扰响应，在准正则模频谱、波形幅度和相位以及晚期尾波上留下印记。引入参数化的超越特克尔什基框架来捕捉与克尔动力学的可能偏差，但到目前为止，铃宕仅作为一个本征值问题被探索。我们首次在时域中实现了该框架，并使用高斯波包进行了(2 + 1)维散射实验。此方法提供了微扰的完整线性演化，从初始的即时响应到铃宕再到晚期阶段。以频域本征值结果为基准，我们发现低方位数时一致性良好，而高方位数受模式混合影响，限制了提取模式的精度。我们还利用时域波形估计线性化修正势模型中的二次和混合系数，为线性近似的有效性范围提供诊断。除了模式频率，我们表明变形参数会强烈影响铃宕幅度和相位，其趋势可从修正势的近视界结构理解。我们还分析了晚期行为，发现近视界变形使尾指数不变，但可大幅改变幂律衰减的起始点。这些结果表明，时域演化提供了一个互补且灵活的框架，用于测试黑洞微扰理论中参数化的广义相对论偏差。
英文摘要
Modifications to General Relativity can significantly alter the perturbative response of black holes, leaving imprints on quasinormal-mode spectra, waveform amplitudes and phases, and late-time tails. The parametrized beyond-Teukolsky framework was introduced to capture possible deviations from Kerr dynamics, but the ringdown has so far only been explored as an eigenvalue problem. We present the first time-domain implementation of this framework and perform (2+1)-dimensional scattering experiments with Gaussian wave packets. This approach provides the full linear evolution of the perturbation, from the initial prompt response through the ringdown and into the late-time regime. Using frequency-domain eigenvalue results as benchmarks, we find excellent agreement for low azimuthal numbers, while higher azimuthal numbers are affected by mode mixing, which limits the precision of the extracted modes. We further use the time-domain waveforms to estimate quadratic and mixed coefficients within the linearized modified-potential model, providing a diagnostic for the regime of validity of the linear approximation. Beyond mode frequencies, we show that the deformation parameters can strongly affect the ringdown amplitude and phase, with trends that can be understood from the near-horizon structure of the modified potential. We also analyze the late- time behavior, finding that near-horizon deformations leave the tail exponent unchanged but can substantially shift the onset of the power-law decay. These results demonstrate that time-domain evolutions provide a complementary and flexible framework for testing parametrized deviations from General Relativity in black-hole perturbation theory.
Comments16 pages, 11 figures, version published in PRD
Journal refPhys. Rev. D 114, 064060, 2026
