AI 中文总结
本研究构建玩具模型探究度规非局域化扩展变形对黑洞铃振的影响，发现宽零均值空间周期扰动可触发黑洞频域与时域不稳定性，揭示了不稳定性阈值的普适标度关系并给出物理解释。
AI 中文摘要
已有研究表明，黑洞准正则模的频谱对远离势峰的几何局域变形极为敏感。真实天文环境导致的变形会遍布整个空间，而非局限于有限区域，目前尚不清楚遍布时空的空间扩展波动能否产生类似效应。本研究构建了一个玩具模型，探究度规变形非局域化且遍布整个空间的情况，研究其如何在时域改变黑洞的铃振阶段。以Pöschl-Teller势和Regge-Wheeler势为代表性背景，研究表明，足够宽的零均值空间周期扰动不仅能在频域触发“频谱不稳定性”，还能在时域触发黑洞不稳定性。通过数值分析，揭示了不稳定性阈值的普适标度关系，并进一步为其物理起源提供了解析解释。
英文摘要
It has been shown that the spectrum of black hole quasi-normal modes is extremely sensitive to localized deformations of the geometry away from the potential peak. The deformation caused by a real astronomical environment will extend throughout the whole space rather than be localized in a finite region. Whether spatially extended fluctuations distributed throughout spacetime can produce similar effects remains unclear. In this work, we construct a toy model to investigate the case that the deformation of the metric is not localized but extends throughout the whole space. We study how it changes the ringdown stage of the black hole in the time domain. Using both the Pöschl-Teller and Regge-Wheeler potentials as representative backgrounds, we show that sufficiently wide spatially periodic perturbations of zero mean can trigger not only the ``spectral instability'' in the frequency domain but also black hole instabilities in the time domain. Through numerical analysis, we uncover a universal scaling relation for the instability threshold and further provide an analytical interpretation of its physical origin.
Comments10 pages, 7 figures, 2 tables
