膜世界扰动的伪谱
Pseudospectrum of Braneworld Perturbations
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- Lanzhou University（兰州大学）
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中文总结 AI 辅助
本文首次将伪谱分析应用于膜世界张量引力扰动，提出双曲形式化与高度函数规范，发现高泛音和零模的谱敏感性高于基模，揭示了膜世界准正规模谱的稳定性特征。
中文摘要 AI 辅助
伪谱分析为探测非自伴算子的谱稳定性提供了一种强有力的方法，并已在黑洞物理中得到广泛应用，但其在膜世界场景中的应用尚未被探索。在本工作中，我们将该方法应用于一个具有代表性的标量场生成的厚膜背景中的张量引力扰动。据我们所知，我们首次提出了膜世界扰动的双曲形式化，并提出了一种适应于翘曲几何的高度函数规范。这种构造将准正规模的出射边界条件转化为有限紧致边界上的正则性条件，并将扰动方程重新表述为由非自伴双曲演化算子生成的一阶系统。利用相应的能量范数，我们计算了局域引力子零模和准正规模谱的条件数和伪谱。我们发现，条件数沿着泛音序列迅速增长，相应的伪谱等高线在高泛音区域形成宽广且连通的结构。这些结果表明了一种强烈的模式依赖的谱敏感性：在所分析的阻尼模式中，较高的泛音不如基模稳健。零模的条件数也大于基模，表明更强的局部一阶敏感性。这些诊断表征了对一般范数有界算子扰动的敏感性。将这种敏感性与特定的膜世界变形联系起来，需要相应的自洽扰动约束。
英文摘要
Pseudospectral analysis provides a powerful way to probe the spectral stability of non-self-adjoint operators and has been widely used in black hole physics, but its application to braneworld scenarios has not yet been explored. In this work, we apply this method to tensor gravitational perturbations in a representative scalar-field-generated thick brane background. To the best of our knowledge, we provide the first hyperboloidal formulation of braneworld perturbations and propose a height-function gauge adapted to the warped geometry. This construction converts the outgoing boundary conditions of quasinormal modes into regularity conditions at finite compactified boundaries and recasts the perturbation equation as a first-order system generated by a non-self-adjoint hyperboloidal evolution operator. With the corresponding energy norm, we compute the condition numbers and pseudospectra of the localized graviton zero mode and the quasinormal-mode spectrum. We find that the condition numbers grow rapidly along the overtone sequence and that the corresponding pseudospectral contours develop broad, connected structures in the high-overtone region. These results show a strongly mode-dependent spectral sensitivity: among the damped modes analyzed, the higher overtones are less robust than the fundamental mode. The zero mode also has a larger condition number than the fundamental mode, indicating stronger local first-order sensitivity. These diagnostics characterize sensitivity to generic norm-bounded operator perturbations. Relating that sensitivity to a specific braneworld deformation requires the corresponding self-consistent perturbation constraints.
