论文标题
伪谱和黑洞准正常模式（IN）稳定性
Pseudospectrum and black hole quasi-normal mode (in)stability
论文作者
论文摘要
我们通过伪谱分析研究了准模式（QNM）在渐近平坦的黑洞空位中的稳定性。 Schwarzschild QNM伪谱的构建揭示了以下内容：（i）在涉及渐近结构的扰动下，最慢的QNM的稳定性重新评估了Nollert讨论的基本QNM的不稳定性[H. P. Nollert，关于黑洞的准模式的重要性，物理。 Rev. D 53，4397（1996）]作为“红外”效应； （ii）在足够高频率的小规模（“紫外线”）下，所有泛音的不稳定性，这些扰动频率足够高，这些扰动朝着沿伪pecterra边界迁移到通用的QNM分支，阐明了诺尔特的先锋工作，诺勒特和诺勒特和价格分析[H. P. Nollert和R. H. Price，《量化准模式系统的激发》，J。Math。物理。 （N.Y.）40，980（1999）]。从方法上讲，采用压缩的倍曲面方法来施放QNM，以非自动辅助操作员的光谱问题进行QNM。在这种情况下，光谱（IN）稳定性自然通过伪观念概念来解决，即我们通过Chebyshev光谱方法和促进引力物理学中的数值构建。在说明了PöschlTeller电位的方法之后，我们解决了Schwarzschild Black Hole案例，其中QNM（IN）稳定性在重力波物理学中的黑洞光谱范围内与物理相关，并且可以想象，当探针中探测到基本的高频时空时空波动，在斑块尺度上。
We study the stability of quasinormal modes (QNM) in asymptotically flat black hole spacetimes by means of a pseudospectrum analysis. The construction of the Schwarzschild QNM pseudospectrum reveals the following: (i) the stability of the slowest-decaying QNM under perturbations respecting the asymptotic structure, reassessing the instability of the fundamental QNM discussed by Nollert [H. P. Nollert, About the Significance of Quasinormal Modes of Black Holes, Phys. Rev. D 53, 4397 (1996)] as an "infrared" effect; (ii) the instability of all overtones under small-scale ("ultraviolet") perturbations of sufficiently high frequency, which migrate towards universal QNM branches along pseudospectra boundaries, shedding light on Nollert's pioneer work and Nollert and Price's analysis [H. P. Nollert and R. H. Price, Quantifying Excitations of Quasinormal Mode Systems, J. Math. Phys. (N.Y.) 40, 980 (1999)]. Methodologically, a compactified hyperboloidal approach to QNMs is adopted to cast QNMs in terms of the spectral problem of a non-self-adjoint operator. In this setting, spectral (in)stability is naturally addressed through the pseudospectrum notion that we construct numerically via Chebyshev spectral methods and foster in gravitational physics. After illustrating the approach with the Pöschl-Teller potential, we address the Schwarzschild black hole case, where QNM (in)stabilities are physically relevant in the context of black hole spectroscopy in gravitational-wave physics and, conceivably, as probes into fundamental high-frequency spacetime fluctuations at the Planck scale.
