再论广义Schwarzschild-Tangherlini拟正规模$D$
Schwarzschild-Tangherlini quasinormal modes at large $D$ revisited
摘要：
广义相对论的大维极限（$D$）已被用于涉及黑洞的问题中作为分析近似工具。此外，有人提出，涉及黑洞的线性和非线性问题都可以在$1/D$展开中系统地研究。在大$D$极限下，利用模式函数的$1/D$展开，研究了含$ω\sim \mathcal{O}(1)$的高维Schwarzschild黑洞的某些准正规模.在本文中，我们重新审视这个线性扰动问题，并获得了一个解析方程的矢量拟正规模式$ω\sim \mathcal{O}(1)$在大$D$极限，而不使用$1/D$展开的模式功能。这可用于计算$1/D$中紧挨着前导阶的拟正规模。在大的$D$极限下，我们还用拉普拉斯变换方法中的$ω\sim \mathcal{O}(D)$计算了矢量和标量拟正规模。我们讨论了这种方法的有用功能，特别是在大$D$限制。
英文摘要：
The large dimension ($D$) limit of general relativity has been used in problems involving black holes as an analytical approximation tool. Further it has been proposed that both linear and nonlinear problems involving black holes can be systematically studied in a $1/D$ expansion. Certain quasinormal modes of higher-dimensional Schwarzschild black holes with $ω\sim \mathcal{O}(1)$ were studied in the large $D$ limit using a $1/D$ expansion for the mode function. In this paper, we revisit this linear perturbation problem and obtain an analytical equation for the vector quasinormal modes $ω\sim \mathcal{O}(1)$ in the large $D$ limit, without using a $1/D$ expansion for the mode function. This can be used to compute quasinormal modes to next to leading order in $1/D$. We also compute vector and scalar quasinormal modes with $ω\sim \mathcal{O}(D)$ in the Laplace transform approach in the large $D$ limit. We discuss the useful features of this approach specifically in the large $D$ limit.
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