Confluent conformal blocks and the Teukolsky master equation
arXiv:1906.10638 · doi:10.1103/PhysRevD.102.105013
Abstract
Quasinormal modes of usual, four dimensional, Kerr black holes are described by certain solutions of a confluent Heun differential equation. In this work, we express these solutions in terms of the connection matrices for a Riemann-Hilbert problem, which was recently solved in terms of the Painlevé V transcendent. We use this formulation to generate the small-frequency expansion for the angular spheroidal harmonic eigenvalue, and derive conditions on the monodromy properties for the radial modes. Using exponentiation, we relate the accessory parameter to a semi-classical conformal description and discuss the properties of the operators involved. For the radial equation, while the operators at the horizons have Liouville momenta proportional to the entropy intake, we find that spatial infinity is described by a Whittaker operator.
arXiv commentREVTeX4.2, 17 pages
References in corpus (28)
- Observation of Gravitational Waves from a Binary Black Hole Merger
- First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole
- Quasinormal modes of black holes and black branes
- Liouville Correlation Functions from Four-dimensional Gauge Theories
- On gravitational-wave spectroscopy of massive black holes with the space interferometer LISA
- Eigenvalues and eigenfunctions of spin-weighted spheroidal harmonics in four and higher dimensions
- On combinatorial expansion of the conformal blocks arising from AGT conjecture
- Witten Diagrams Revisited: The AdS Geometry of Conformal Blocks
- Darboux coordinates, Yang-Yang functional, and gauge theory
- Asymptotically free N=2 theories and irregular conformal blocks
- Classical Conformal Blocks and Painleve VI
- How instanton combinatorics solves Painlevé VI, V and III's
- Isomonodromic tau-functions from Liouville conformal blocks
- Conformal field theory of Painlevé VI
- Black Hole Scattering from Monodromy
- Fredholm determinant and Nekrasov sum representations of isomonodromic tau functions
- Self-Force Calculations with Matched Expansions and Quasinormal Mode Sums
- Black Hole Monodromy and Conformal Field Theory
- Conformal field theory on the plane
- Isomonodromy, Painlevé Transcendents and Scattering off of Black Holes
- Irregular conformal blocks and connection formulae for Painlevé V functions
- Greybody factors at large imaginary frequencies
- Kerr-de Sitter Quasinormal Modes via Accessory Parameter Expansion
- Scalar quasinormal modes of Kerr-AdS
- Irregular conformal blocks, with an application to the fifth and fourth Painlevé equations
- Confluent primary fields in the conformal field theory
- Resurgence, Painleve Equations and Conformal Blocks
- A Riemann-Hilbert Approach to the Heun Equation
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- Exact solution of Kerr black hole perturbations via CFT and instanton counting. Greybody factor, Quasinormal modes and Love numbers
- Irregular Liouville correlators and connection formulae for Heun functions
- CFT description of BH's and ECO's: QNMs, superradiance, echoes and tidal responses
- Perturbative connection formulas for Heun equations
- A slow review of the AGT correspondence
- Teukolsky master equation and Painlevé transcendents: numerics and extremal limit
- Accessory parameters in confluent Heun equations and classical irregular conformal blocks
- Scalar quasi-normal modes of accelerating Kerr-Newman-AdS black holes
- Scalar/Dirac perturbations of the Reissner-Nordström black hole and Painlevé transcendents
- Quantum spectral problems and isomonodromic deformations
- Emptiness formation probability and Painlevé V equation in the XY spin chain
- Massive scalar perturbations in Kerr Black Holes: near extremal analysis
- Elementary Integral Series for Heun Functions. With an Application to Black-Hole Perturbation Theory
- Expansions for semiclassical conformal blocks
- More on the SW-QNM correspondence
- Machine Learning-Based Analytical Expressions for Gray-Body Factors and Application to Primordial Black Holes
- Remarks on holographic models of the Kerr-AdS geometry
- Isomonodromy sets of accessory parameters for Heun class equations
- Spectral Problems for Quasinormal Modes of Black Holes
- Ergodic Hysteresis of the Kerr black hole spectrum