Isomonodromy, Painlevé Transcendents and Scattering off of Black Holes

Abstract

We apply the method of isomonodromy to study the scattering of a generic Kerr-NUT-(A)dS black hole. For generic values of the charges, the problem is related to the connection problem of the Painlevé VI transcendent. We review a few facts about Painlevé VI, Garnier systems and the Hamiltonian structure of flat connections in the Riemann sphere. We then outline a method for computing the scattering amplitudes based on Hamilton-Jacobi structure of Painlevé, and discuss the implications of the generic result to black hole complementarity.

arXiv comment40 pages, 4 figures, JHEP style

References in corpus (20)

• Quasinormal modes of black holes and black branes
• Eternal Black Holes in AdS
• Liouville Correlation Functions from Four-dimensional Gauge Theories
• Structure Constants and Conformal Bootstrap in Liouville Field Theory
• Viscosity, Black Holes, and Quantum Field Theory
• The Black Hole Singularity in AdS/CFT
• On combinatorial expansion of the conformal blocks arising from AGT conjecture
• Darboux coordinates, Yang-Yang functional, and gauge theory
• Perturbations of Kerr-de Sitter Black Hole and Heun's Equations
• Separability of Hamilton-Jacobi and Klein-Gordon Equations in General Kerr-NUT-AdS Spacetimes
• A direct proof of AGT conjecture at beta = 1
• Conformal field theory of Painlevé VI
• Black Hole Scattering from Monodromy
• Gravitational quasinormal modes for Kerr Anti-de Sitter black holes
• Stability of the Cauchy horizon in Kerr--de Sitter spacetimes
• Heun equation, Teukolsky equation, and type-D metrics
• On the parameters of the Kerr-NUT-(anti-)de Sitter space-time
• Tabulation of PVI Transcendents and Parametrization Formulas (August 17, 2011)
• The analytic solution for the power series expansion of Heun function
• Hidden Symmetries and Black Holes

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• Irregular conformal blocks and connection formulae for Painlevé V functions
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• Kerr-de Sitter Quasinormal Modes via Accessory Parameter Expansion
• Perturbative connection formulas for Heun equations
• Scalar quasinormal modes of Kerr-AdS${}_5$
• Confluent conformal blocks and the Teukolsky master equation
• Warped Symmetries of the Kerr Black Hole
• Exact thermal correlators of holographic $CFT$s
• Classical Conformal Blocks and Accessory Parameters from Isomonodromic Deformations
• Teukolsky master equation and Painlevé transcendents: numerics and extremal limit
• Accessory parameters in confluent Heun equations and classical irregular conformal blocks
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• Massive scalar perturbations in Kerr Black Holes: near extremal analysis
• On the Existence of Monodromies for the Rabi model
• Expansions for semiclassical conformal blocks
• Absorption cross section in gravity's rainbow from confluent Heun equation
• Emergent Black Hole Thermodynamics from Monodromy
• More on the SW-QNM correspondence
• Classical conformal blocks, Coulomb gas integrals and Richardson-Gaudin models
• Spectral Problems for Quasinormal Modes of Black Holes
• Ergodic Hysteresis of the Kerr black hole spectrum