Teukolsky master equation and Painlevé transcendents: numerics and extremal limit

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 Painlevé 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 Painlevé V and III transcendents.

REVTeX 4.2, 17 pages, 7 figures; version 2 with added references and better control of the Stokes phenomenon in the numerical calculations. Results now agree within machine precision to the method of choice when they are both applicable

References in corpus (8)

• Slow relaxation of rapidly rotating black holes
• Self-Force Calculations with Matched Expansions and Quasinormal Mode Sums
• Isomonodromy, Painlevé Transcendents and Scattering off of Black Holes
• Greybody factors at large imaginary frequencies
• Synchronous frequencies of extremal Kerr black holes: resonances, scattering and stability
• Spectroscopy of Extremal (and Near-Extremal) Kerr Black Holes
• Accessory parameters in confluent Heun equations and classical irregular conformal blocks
• Quantum spectral problems and isomonodromic deformations

Cited by in corpus (14)

• Irregular Liouville correlators and connection formulae for Heun functions
• Black hole perturbation theory and multiple polylogarithms
• Scalar/Dirac perturbations of the Reissner-Nordström black hole and Painlevé transcendents
• Exceptional point and hysteresis in perturbations of Kerr black holes
• Quasinormal modes and excitation factors of Kerr black holes
• Massive scalar perturbations in Kerr Black Holes: near extremal analysis
• Expansions for semiclassical conformal blocks
• New Chandrasekhar transformation in Kerr spacetime
• Global study of the scalar quasi-normal modes of Kerr-AdS${}_5$ black holes: Stability, thermality, and horizon area quantization
• More on the SW-QNM correspondence
• Notes on Quasinormal Modes of charged de Sitter Blackholes from Quiver Gauge Theories
• Connection formulae in the Collision Limit I: Case Studies in Lifshitz Geometry
• Spectral Problems for Quasinormal Modes of Black Holes
• Ergodic Hysteresis of the Kerr black hole spectrum