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arXiv · 2105.08790

Teukolsky master equation and Painlev\'e transcendents: numerics and extremal limit

Bruno Carneiro da Cunha·João Paulo Cavalcante
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Abstract

We conduct an analysis of the quasi-normal modes for generic spin perturbations of the Kerr black hole using the isomonodromic method. The strategy consists of solving the Riemann-Hilbert map relating the accessory parameters of the differential equations involved to monodromy properties of the solutions, using the $\tau$-function for the Painlev\'e V transcendent. We show good accordance of the method with the literature for generic rotation parameter $a<M$. In the extremal limit, we determined the dependence of the modes with the black hole temperature and establish that the extremal values of the modes are obtainable from the Painlev\'e V and III transcendents.

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Bruno Carneiro da Cunha, João Paulo Cavalcante. 2021-05-18. Teukolsky master equation and Painlev\'e transcendents: numerics and extremal limit. https://doi.org/10.1103/physrevd.104.084051

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