Black hole perturbation theory and multiple polylogarithms
Black hole perturbation theory and multiple polylogarithms
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DOI：
10.1007/jhep11(2023)059
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发表时间：
2023-07
影响因子：
5.4
通讯作者：
G. Aminov;Paolo Arnaudo;G. Bonelli;A. Grassi;A. Tanzini
中科院分区：
文献类型：
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作者：
G. Aminov;Paolo Arnaudo;G. Bonelli;A. Grassi;A. Tanzini
我们在四维史瓦西（反）德西特背景下研究黑洞线性微扰理论。当处理正宇宙常数时，相应的谱问题可以通过 Nekrasov-Shatashvili 函数或等效的经典 Virasoro 共形块系统地解决。然而，如果宇宙常数为负，则对于某些扰动，这种方法的实施可能会更加复杂。对于这些情况，我们提出了一种替代方法，以分析的方式建立小黑洞和大黑洞的微扰理论。我们的分析揭示了一种涉及多个多对数的新的底层递归结构。我们专注于狄利克雷和罗宾边界条件下的引力、电磁和共形耦合标量扰动。详细研究了重力摄动标量扇区的低洼模式及其流体动力极限。
We study black hole linear perturbation theory in a four-dimensional Schwarzschild (anti) de Sitter background. When dealing with a positive cosmological constant, the corresponding spectral problem is solved systematically via the Nekrasov-Shatashvili functions or, equivalently, classical Virasoro conformal blocks. However, this approach can be more complicated to implement for certain perturbations if the cosmological constant is negative. For these cases, we propose an alternative method to set up perturbation theory for both small and large black holes in an analytical manner. Our analysis reveals a new underlying recursive structure that involves multiple polylogarithms. We focus on gravitational, electromagnetic, and conformally coupled scalar perturbations subject to Dirichlet and Robin boundary conditions. The low-lying modes of the scalar sector of gravitational perturbations and its hydrodynamic limit are studied in detail.