AI 中文总结
研究史瓦西 - 反德西特黑洞上无质量标量场准正则模，用切比雪夫谱方法，通过变形反德西特边界条件研究其谱特性，发现非狄利克雷值下有边界条件诱导的不稳定额外模式及近狄利克雷细化未发现有限临界角。
AI 中文摘要
我们使用切比雪夫谱方法研究四维史瓦西 - 反德西特黑洞上最小耦合无质量标量场的准正则模。在紧致化外部区域后，径向问题被表述为无量纲频率下的二次矩阵束。对于共形反德西特边界处的标准狄利克雷（或零场）边界条件，我们重现了跨越小、中、大黑洞的已知标量谱。然后通过在无质量标量的两个独立渐近系数之间施加广义关系来变形反德西特边界条件，这种变形被视为无质量标量的广义系数边界条件。狄利克雷端点恢复了稳定的标准谱，对于每个非狄利克雷值以及代表性的小、中、大黑洞，我们发现了一个具有正虚部的额外模式，表明边界条件诱导的不稳定性。近狄利克雷细化在探测到的最小变形下未发现有限临界角。
英文摘要
We study quasinormal modes (QNMs) of a minimally coupled massless scalar field on four-dimensional Schwarzschild--anti-de Sitter black holes using a Chebyshev spectral method. After compactifying the exterior domain, the radial problem is formulated as a quadratic matrix pencil in the dimensionless frequency. For the standard Dirichlet, or vanishing-field, boundary condition at the conformal AdS boundary, we reproduce the known scalar spectra across small, intermediate, and large black holes, including long overtone sequences and the expected approach to pure-AdS normal modes in the small black hole limit. We then deform the AdS boundary condition by imposing a generalized relation between the two independent asymptotic coefficients of the massless scalar. This deformation is treated as a generalized coefficient boundary condition for the massless scalar, and not as the usual alternative quantization for scalars in the Breitenlohner-Freedman window. The Dirichlet endpoint recovers the stable standard spectrum. For every non-Dirichlet value examined, and for representative small, intermediate, and large black holes, we find an additional mode with positive imaginary part, signaling a boundary-condition-induced instability. A near-Dirichlet refinement finds no finite critical angle down to the smallest deformation probed.
Comments24 pages, 3 figures
