Abstract
We study linear scalar perturbations of slowly accelerating Kerr-Newman-anti-de Sitter black holes using the method of isomonodromic deformations. The conformally coupled Klein-Gordon equation separates into two second-order ordinary differential equations with five singularities. Nevertheless, the angular equation can be transformed into a Heun equation, for which we provide an asymptotic expansion for the angular eigenvalues in the small acceleration and rotation limit. In the radial case, we recast the boundary value problem in terms of a set of initial conditions for the isomonodromic tau function of Fuchsian systems with five regular singular points. For the sake of illustration, we compute the quasi-normal modes frequencies.
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Acknowledgments
This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2022R1I1A2063176) and the Dongguk University Research Fund of 2023. BG appreciates APCTP for its hospitality during the topical research program, Multi-Messenger Astrophysics and Gravitation. J.B.A. acknowledges Bruno Carneiro da Cunha and João Paulo Cavalcante for stimulating discussions about this work. Finally, we thank the referee for motivating a revision of the previous version of this paper.
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Amado, J.B., Gwak, B. Scalar quasi-normal modes of accelerating Kerr-Newman-AdS black holes. J. High Energ. Phys. 2024, 189 (2024). https://doi.org/10.1007/JHEP02(2024)189
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DOI: https://doi.org/10.1007/JHEP02(2024)189