AI 中文总结
研究利用引力波探测器测试黑洞衰荡光谱，通过分解量子黑洞时域格林函数，阐明其响应与不同QNM集合的关系，发现重建效率与演化阶段有关，为黑洞光谱学和量子黑洞地震学提供统一因果框架。
AI 中文摘要
引力波探测器灵敏度的提高使得对黑洞（BH）衰荡光谱进行越来越精确的测试成为可能。然而，BH 准正则模（QNMs）在频谱上是不稳定的：视界附近的微小变化会产生截然不同的 QNM 光谱，而因果律要求在反射信号返回之前，快速衰荡保持类似 BH 的状态。具有大量内部反射的量子 BH 为这种矛盾提供了一个自然的场景，但其时域波形与不同 QNM 光谱之间的关系仍缺乏一致的描述。在这项工作中，我们系统地研究了量子 BH 的时域格林函数，考虑了位于光环势垒内外的源。通过将格林函数分解为因果上不同的分量，并一致地选择相应的逆拉普拉斯轮廓，我们阐明了响应是如何由不同的 QNM 集合构建的。我们发现，一旦探测到弯曲时空，量子 BH QNM 重建总能如实地描述信号，但其实际效率强烈依赖于演化阶段。在内部反射变得重要之前，我们证明这个基在形式上等同于 BH QNM 和尾项展开，其收敛性质对源位置敏感。在后期，长寿命模提供了一个有效的基。时域模拟证实了这些结果，为 BH 光谱学和量子 BH 地震学提供了一个统一的因果框架。
英文摘要
The growing sensitivity of gravitational-wave detectors enables increasingly precise tests of black hole (BH) ringdown spectroscopy. BH quasinormal modes (QNMs) are, however, spectrally unstable: small near-horizon modifications can produce a drastically different QNM spectrum, while causality requires the prompt ringdown to remain BH-like until the reflected signal returns. Quantum BHs with substantial interior reflection provide a natural setting for this tension, yet the relation between their time-domain waveform and different QNM spectra still lacks a consistent picture. In this work, we systematically examine the time-domain Green function for quantum BHs, considering sources located outside and inside the light-ring potential barrier. By decomposing the Green function into causally distinct components and choosing the corresponding inverse-Laplace contours consistently, we clarify how the response is built from different sets of QNMs. We find that the quantum BH QNM reconstruction always faithfully describes the signal once the curved spacetime is probed, but its practical efficiency depends strongly on the evolutionary stage. Before interior reflection becomes relevant, we prove that this basis is formally equivalent to the BH QNM and tail expansions, with convergence properties sensitive to source location. At late times, the long-lived modes provide an efficient basis. Time-domain simulations confirm these results, providing a unified causal framework for BH spectroscopy and quantum BH seismology.
Comments30 pages, 11 figures
