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Article
Report number	arXiv:2307.10141
Title	Black hole perturbation theory and multiple polylogarithms
Author(s)	Aminov, Gleb (SUNY, Stony Brook ; Stony Brook U., New York, SCGP) ; Arnaudo, Paolo (SISSA, Trieste ; INFN, Trieste ; Trieste U., DMI) ; Bonelli, Giulio (SISSA, Trieste ; INFN, Trieste ; Trieste U., DMI) ; Grassi, Alba (CERN ; Geneva U.) ; Tanzini, Alessandro (SISSA, Trieste ; INFN, Trieste ; Trieste U., DMI)
Publication	2023-11-10
Imprint	2023-07-19
Number of pages	58
Note	Version 2 has 58 pages, 3 figures, and 4 Mathematica files. Minor corrections added. Comments welcome
In:	JHEP 2311 (2023) 059
DOI	10.1007/JHEP11(2023)059
Subject category	math.MP ; Mathematical Physics and Mathematics ; math-ph ; Mathematical Physics and Mathematics ; gr-qc ; General Relativity and Cosmology ; hep-th ; Particle Physics - Theory
Abstract	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.
Copyright/License	preprint: (License: arXiv nonexclusive-distrib 1.0) publication: © 2023-2024 The Authors (License: CC-BY-4.0), sponsored by SCOAP³

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