Exact solution of Kerr black hole perturbations via CFT${}_2$ and instanton counting. Greybody factor, Quasinormal modes and Love numbers

Abstract

We give explicit expressions for the finite frequency greybody factor, quasinormal modes and Love numbers of Kerr black holes by computing the exact connection coefficients of the radial and angular parts of the Teukolsky equation. This is obtained by solving the connection problem of the confluent Heun equation in terms of the explicit expression of irregular Virasoro conformal blocks as sums over partitions via the AGT correspondence. In the relevant approximation limits our results are in agreement with existing literature. The method we use can be extended to solve the linearized Einstein equation in other interesting gravitational backgrounds.

arXiv comment37 pages, 7 figures, comments welcome

References in corpus (49)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• Quasinormal modes of black holes and black branes
• Liouville Correlation Functions from Four-dimensional Gauge Theories
• Constraining neutron star tidal Love numbers with gravitational wave detectors
• Structure Constants and Conformal Bootstrap in Liouville Field Theory
• The Kerr/CFT Correspondence
• New N=2 Superconformal Field Theories in Four Dimensions
• Two and three-point functions in Liouville theory
• Loop and surface operators in N=2 gauge theory and Liouville modular geometry
• Instantons and recursion relations in N=2 Susy gauge theory
• Eigenvalues and eigenfunctions of spin-weighted spheroidal harmonics in four and higher dimensions
• Testing strong-field gravity with tidal Love numbers
• Quantization of Integrable Systems and Four Dimensional Gauge Theories
• On the Liouville three-point function
• Multi-Instanton Calculus and Equivariant Cohomology
• Universal Low-Energy Dynamics for Rotating Black Holes
• Black hole stereotyping: Induced gravito-static polarization
• Tidal Deformation and Dissipation of Rotating Black Holes
• On non-conformal limit of the AGT relations
• Asymptotically free N=2 theories and irregular conformal blocks
• Spinning Black Holes Fall in Love
• Tidal Love Numbers of Kerr Black Holes
• Wild Quiver Gauge Theories
• Irregular singularities in Liouville theory
• Classical Conformal Blocks and Painleve VI
• Matone's Relation in the Presence of Gravitational Couplings
• Instanton counting with a surface operator and the chain-saw quiver
• How instanton combinatorics solves Painlevé VI, V and III's
• On Painlevé/gauge theory correspondence
• On Combinatorial Expansions of Conformal Blocks
• Vertices, Vortices & Interacting Surface Operators
• 3d & 5d gauge theory partition functions as q-deformed CFT correlators
• QNMs of branes, BHs and fuzzballs from Quantum SW geometries
• Black-hole microstate spectroscopy: ringdown, quasinormal modes, and echoes
• Kerr-de Sitter Greybody Factors via Isomonodromy
• Quasinormal modes of Kerr-de Sitter black holes via the Heun function
• Irregular conformal blocks and connection formulae for Painlevé V functions
• Kerr-de Sitter Quasinormal Modes via Accessory Parameter Expansion
• Irregular conformal blocks, with an application to the fifth and fourth Painlevé equations
• Confluent conformal blocks and the Teukolsky master equation
• Black hole evaporation in de Sitter space
• BPS relations from spectral problems and blowup equations
• Painleve equations from Nakajima-Yoshioka blowup relations
• Accessory parameters in confluent Heun equations and classical irregular conformal blocks
• Quantum spectral problems and isomonodromic deformations
• Instantons to the people: the power of one-form symmetries
• Stokes phenomenon and Hawking Radiation
• Remarks on holographic models of the Kerr-AdS${}_5$ geometry
• Greybody factors for a black hole in massive gravity

Cited by in corpus (57)

• Irregular Liouville correlators and connection formulae for Heun functions
• Love symmetry
• CFT description of BH's and ECO's: QNMs, superradiance, echoes and tidal responses
• Ringdown stability: greybody factors as stable gravitational-wave observables
• Holographic thermal correlators from supersymmetric instantons
• Gravitational orbits, double-twist mirage, and many-body scars
• Non-linearities in the tidal Love numbers of black holes
• Black hole perturbation theory and multiple polylogarithms
• Implications of the Weak Gravity Conjecture for Tidal Love Numbers of Black Holes
• Thermal Ringdown of a Kerr Black Hole: Overtone Excitation, Fermi-Dirac Statistics and Greybody Factor
• Scalar Love numbers and Love symmetries of 5-dimensional Myers-Perry black holes
• Black hole superradiance with (dark) matter accretion
• Vanishing Love of Black Holes in General Relativity: From Spacetime Conformal Symmetry of a Two-dimensional Reduced Geometry
• Perturbative connection formulas for Heun equations
• Nonlinear Quasi-Normal Modes: Uniform Approximation
• Ladder Symmetries and Love Numbers of Reissner--Nordström Black Holes
• Turning black-holes and D-branes inside out their photon-spheres
• A Rutherford-like formula for scattering off Kerr-Newman BHs and subleading corrections
• Exact thermal correlators of holographic $CFT$s
• Amplitudes and Polarizations of Quadratic Quasi-Normal Modes for a Schwarzschild Black Hole
• Quasinormal Modes of C-metric from SCFTs
• Exact WKB and the quantum Seiberg-Witten curve for 4d $N=2$ pure $SU(3)$ Yang-Mills, Part I: Abelianization
• Quasinormal Modes and Love Numbers of Kerr Black Holes from AdS${}_2$ Black Holes
• Scalar quasi-normal modes of accelerating Kerr-Newman-AdS black holes
• Quasinormal modes and excitation factors of Kerr black holes
• Aspects of thermal one-point functions and response functions in AdS Black holes
• Quasinormal Modes and Universality of the Penrose Limit of Black Hole Photon Rings
• Exact conditions for Quasi-normal modes of extremal M5-branes and Exact WKB analysis
• Quasi-normal modes for the D3-branes and Exact WKB analysis
• Resumming Post-Minkowskian and Post-Newtonian gravitational waveform expansions
• The ringing of quantum corrected Schwarzschild black hole with GUP
• Expansions for semiclassical conformal blocks
• Duality between Seiberg-Witten Theory and Black Hole Superradiance
• Absorption cross section in gravity's rainbow from confluent Heun equation
• Systematic biases from ignoring environmental tidal effects in gravitational wave observations
• New Chandrasekhar transformation in Kerr spacetime
• An analytic approach to quasinormal modes for coupled linear systems
• Complete quasinormal modes of Type-D black holes
• Fermionic Love of Black Holes in General Relativity
• Machine Learning-Based Analytical Expressions for Gray-Body Factors and Application to Primordial Black Holes
• Thermodynamics, magnetic properties, and global $U(1)$ symmetry breaking of the S-type Gubser-Rocha model
• Quantum-Corrected Hawking Radiation from Near-Extremal Kerr-Newman Black Holes
• Kerr-Newman quasinormal modes and Seiberg-Witten theory
• Massive vector field perturbations in the Schwarzschild spacetime from supersymmetric gauge theory
• Dynamical Love Numbers for Black Holes and Beyond from Shell Effective Field Theory
• Quantum Mechanics from General Relativity and the Quantum Friedmann Equation
• Greybody factors of string-corrected d-dimensional black holes
• Connection formulae in the Collision Limit I: Case Studies in Lifshitz Geometry
• Holographic thermal correlators from recursions
• Notes on Quasinormal Modes of charged de Sitter Blackholes from Quiver Gauge Theories
• Gravitational radiations of Kerr black hole from warped symmetries
• Ergodic Hysteresis of the Kerr black hole spectrum
• Exact scalar (quasi-)normal modes of black holes and solitons in gauged SUGRA
• Explorations of Universality in the Entropy and Hawking Radiation of Non-Extremal Kerr AdS${}_4$ Black Holes
• Quasinormal Modes of Extremal Reissner-Nordstrom Black Holes via Seiberg-Witten Quantization
• Extremal Love: tidal/electromagnetic deformability, logarithmic running and the weak gravity conjecture
• Analytic Computation of Dilaton Black Hole Quasinormal Modes via Seiberg-Witten Theory