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.
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Acknowledgments
We would like to thank L. Andersson, E. Barausse, M. Bianchi, J. Bluemlein, V. Cardoso, S. Cecotti, O. Dias, M. Dodelson, F. Fucito, S. Grozdanov, Y. Hatsuda, C. Iossa, R. Karlsson, J.F. Morales, R. Russo, P. Vanhove, S.T. Yau, and A. Zhiboedov for interesting discussions.
The research of G.B. is partly supported by the INFN Iniziativa Specifica ST&FI and by the PRIN project “Non-perturbative Aspects Of Gauge Theories And Strings”. The research of P.A. and A.T. is partly supported by the INFN Iniziativa Specifica GAST. The research of P.A. G.B and A.T. is partly supported by the MIUR PRIN Grant 2020KR4KN2 “String Theory as a bridge between Gauge Theories and Quantum Gravity”. The work of A.G. is partially supported by the Swiss National Science Foundation Grant No.185723 and the NCCR SwissMAP. The work of A.T. is partly supported by the PRIN project “Geometria delle varietà algebriche” and InDAM GNFM.
We acknowledge the Galileo Galilei Institute in Firenze and the participants of the Workshop “New horizons for (no-)horizon physics: from gauge to gravity and back” during which part of this research work was conducted.
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Aminov, G., Arnaudo, P., Bonelli, G. et al. Black hole perturbation theory and multiple polylogarithms. J. High Energ. Phys. 2023, 59 (2023). https://doi.org/10.1007/JHEP11(2023)059
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DOI: https://doi.org/10.1007/JHEP11(2023)059