Black hole perturbation theory and multiple polylogarithms

• Published in: The journal of high energy physics Vol. 2023; no. 11; pp. 59 - 61
• Main Authors: Aminov, Gleb, Arnaudo, Paolo, Bonelli, Giulio, Grassi, Alba, Tanzini, Alessandro
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 10.11.2023; Springer Nature B.V; SpringerOpen
• Subjects: Black Holes; Boundary conditions; Classical and Quantum Gravitation; Classical Theories of Gravity; Cosmological constant; Dirichlet problem; Elementary Particles; High energy physics; Holography and Hydrodynamics; Methods; Perturbation theory; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; String Theory; Supersymmetric Gauge Theory; Theoretical physics; Classical Theories of Gravity; Holography and Hydrodynamics; Black Holes; Supersymmetric Gauge Theory
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP11(2023)059

A bstract 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.