AI 中文总结
本研究采用切比雪夫谱方法，绘制了5至26维下高斯-邦迪修正史瓦西黑洞的三类准正规模式频谱，揭示了高曲率动力学特征与六维张量不稳定性，为相关引力研究提供基准。
AI 中文摘要
我们对高维下带有高斯-邦迪（GB）项修正的史瓦西黑洞的标量、矢量与张量准正规模式（QNM）开展了统一研究。采用高精度切比雪夫谱方法，我们绘制了维度D∈{5,6,7,8,10,11,12,26}下的QNM频谱，该范围远超六阶WKB法与特征积分技术仍可靠的区间。在三种自旋扇区中，我们发现了高曲率动力学的若干稳健特征：过阻尼纯虚模式的出现、高阶泛音实部的非单调行为，以及弦动机维度下无量纲QNM频率的显著放大。在标量与矢量扇区中，我们发现当GB耦合为零时，标量单极（ℓ=0）与矢量偶极（ℓ=1）间存在精确等谱性，并基于对应哈密顿量的达布克斯分解提供了解析证明。在张量扇区中，我们首次数值证实了六维下长期预测的不稳定性；其 onset 由Cohn-Calogero界精确捕捉，得出质量阈值GM≤158.1 α^(3/2)。在D≥7时未发现类似不稳定性，也不存在张量等谱性。将无量纲频率转换为物理单位后表明，高维下被放大的模式可能进入未来天基探测器（如DECIGO）的灵敏度窗口。该合并分析为爱因斯坦-高斯-邦迪引力中的QNM提供了全面基准，并凸显了强耦合与高阶泛音区域标准近似方案的局限性。
英文摘要
We present a unified study of scalar, vector, and tensor quasinormal modes (QNMs) of Schwarzschild black holes corrected by a Gauss--Bonnet (GB) term in higher dimensions. Using a high-precision Chebyshev spectral method, we map the QNM spectra across $D\in\{5,6,7,8,10,11,12,26\}$ well beyond the regime where sixth-order WKB and characteristic-integration techniques remain reliable. Across the three spin sectors, we find several robust signatures of higher-curvature dynamics: the appearance of overdamped purely imaginary modes, non-monotonic behaviour in the real parts of higher overtones, and a strong amplification of the dimensionless QNM frequencies in string-motivated dimensions. In the scalar and vector sectors, we uncover an exact isospectrality between the scalar monopole ($\ell=0$) and vector dipole ($\ell=1$) at vanishing GB coupling, and we provide an analytic proof based on a Darboux factorisation of the corresponding Hamiltonians. In the tensor sector, we obtain the first numerical confirmation of the long-predicted instability in six dimensions; its onset is sharply captured by the Cohn--Calogero bound and leads to the mass threshold $GM\leq 158.1\,α^{3/2}$. No analogous instability is found for $D\geq 7$, and no tensor isospectrality occurs. Converting the dimensionless frequencies to physical units suggests that the amplified modes in higher dimensions may enter the sensitivity window of future space-based detectors such as DECIGO. The merged analysis provides a comprehensive benchmark for QNMs in Einstein--Gauss--Bonnet gravity and highlights the limitations of standard approximation schemes in the strong-coupling and high-overtone regimes.
Comments92 pages, 26 figures
Journal refPhys. Rev. D 114, 044015 (2026)
