Quasinormal modes of black holes and Borel summation

Abstract

We propose a simple and efficient way to compute quasinormal frequencies of spherically symmetric black holes. We revisit an old idea that relates them to bound state energies of anharmonic oscillators by an analytic continuation. This connection enables us to achieve remarkable high-order computations of WKB series by Rayleigh-Schrödinger perturbation theory. The known WKB results are easily reproduced. Our analysis shows that the perturbative WKB series of the quasinormal frequencies turn out to be Borel summable divergent series both for the Schwarzschild and for the Reissner-Nordström black holes. Their Borel sums reproduce the correct numerical values.

arXiv comment15 pages, v2: references added, Mathematica codes are included in the source file

References in corpus (22)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• GW151226: Observation of Gravitational Waves from a 22-Solar-Mass Binary Black Hole Coalescence
• Quasinormal modes of black holes and black branes
• Quasi-Normal Modes of Stars and Black Holes
• Tests of general relativity with GW150914
• Quasinormal modes of black holes: from astrophysics to string theory
• Quasinormal behavior of the D-dimensional Schwarzshild black hole and higher order WKB approach
• Higher order WKB formula for quasinormal modes and grey-body factors: recipes for quick and accurate calculations
• Quasinormal modes of black holes. The improved semianalytic approach
• Eigenvalues and eigenfunctions of spin-weighted spheroidal harmonics in four and higher dimensions
• Lectures on non-perturbative effects in large N gauge theories, matrix models and strings
• A Primer on Resurgent Transseries and Their Asymptotics
• Parametrized black hole quasinormal ringdown. I. Decoupled equations for nonrotating black holes
• The asymptotic quasinormal mode spectrum of non-rotating black holes
• Asymptotic Quasinormal Frequencies for Black Holes in Non-Asymptotically Flat Spacetimes
• Quasinormal modes of maximally charged black holes
• Cheshire Cat resurgence, Self-resurgence and Quasi-Exact Solvable Systems
• Deconstructing zero: resurgence, supersymmetry and complex saddles
• Resumming the string perturbation series
• Holomorphic Anomaly and Quantum Mechanics
• Some exact quasi-normal frequencies of a massless scalar field in the Schwarzschild space-time
• Reply to "Comment on `Some exact quasinormal frequencies of a massless scalar field in Schwarzschild spacetime' ''

Cited by in corpus (70)

• Quasinormal ringing of regular black holes in asymptotically safe gravity: the importance of overtones
• Wormholes without exotic matter: quasinormal modes, echoes and shadows
• Quasinormal modes and Hawking radiation of black holes in cubic gravity
• Black holes in galactic centers: quasinormal ringing, grey-body factors and Unruh temperature
• Investigating the Connection between Generalized Uncertainty Principle and Asymptotically Safe Gravity in Black Hole Signatures through Shadow and Quasinormal Modes
• Long-lived quasinormal modes and overtones' behavior of the holonomy corrected black holes
• Topical Review: Greybody Factors and Quasinormal Modes for Black Holes in Various Theories -- Fingerprints of Invisibles
• Quasinormal Modes of Black holes in $f(Q)$ gravity
• Quasinormal modes of renormalization group improved Dymnikova regular black holes
• Quasinormal modes of black holes in f(T) gravity
• Quasinormal modes and grey-body factors of regular black holes with a scalar hair from the Effective Field Theory
• Slowly-rotating curved acoustic black holes: Quasinormal modes, Hawking-Unruh radiation and quasibound states
• Quasinormal modes of Kerr-de Sitter black holes via the Heun function
• Quasinormal modes of massive scalar fields in four-dimensional wormholes: anomalous decay rate
• Massive Dirac quasinormal modes in Schwarzschild-dS black holes: anomalous decay rate and fine structure
• Quasinormal modes in higher derivative gravity: testing the black hole parametrization and sensitivity of overtones
• Vanishing Love of Black Holes in General Relativity: From Spacetime Conformal Symmetry of a Two-dimensional Reduced Geometry
• Quasinormal modes of an improved Schwarzschild black hole
• Quasinormal modes of Schwarzschild black holes on the real axis
• Regular charged black holes, energy conditions and quasinormal modes
• Anomalous decay rate of quasinormal modes in Reissner-Nordström black holes
• Analytic formula for quasinormal modes in the near-extreme Kerr-Newman-de Sitter spacetime governed by a non-Pöschl-Teller potential
• Quasi-normal modes of the Einstein-Maxwell-aether Black Hole
• Quasinormal modes and their anomalous behavior for black holes in $f(R)$ gravity
• Quasinormal modes in the field of a dyon-like dilatonic black hole
• Lessons from black hole quasinormal modes in modified gravity
• Anomalous decay rate of quasinormal modes
• Quasinormal Modes of Charged Fields in Reissner-Nordstrom Backgrounds by Borel-Pade Summation of Bender-Wu Series
• Quasinormal ringing of general spherically symmetric parametrized black holes
• Black holes in Einstein-aether theory: Quasinormal modes and time-domain evolution
• Conformal Weyl gravity via two stages of quasinormal ringing and late-time behavior
• Photonsphere, shadow, quasinormal modes, and greybody bounds of non-rotating Simpson-Visser black hole
• Accurate Quasinormal Modes of the Five-Dimensional Schwarzschild-Tangherlini Black Holes
• Semi-analytic expressions for quasinormal modes of slowly rotating Kerr black holes
• Ringing and echoes from black bounces surrounded by the string cloud
• Quasinormal Modes of C-metric from SCFTs
• Quasinormal modes of charged black holes in higher-dimensional Einstein-power-Maxwell theory
• Quasinormal modes of dirty black holes in the two-loop renormalizable effective gravity
• Quasinormal modes of a massive scalar field nonminimally coupled to gravity in the spacetime of Self-Dual Black Hole
• Causality and quasi-normal modes in the GREFT
• Black Hole Perturbations and Quasinormal Modes in Hybrid Metric-Palatini Gravity
• Overtones' outburst and Hawking evaporation of Kazakov-Solodukhin quantum corrected black hole
• Quasinormal modes of black holes encircled by a gravitating thin disk
• Quasinormal modes and self-adjoint extensions of the Schroedinger operator
• On quasinormal modes in 4D black hole solutions in the model with anisotropic fluid
• Quasinormal modes of the Bardeen black hole with a cloud of strings
• Resurgence in Lorentzian quantum cosmology: No-boundary saddles and resummation of quantum gravity corrections around tunneling saddle points
• Quasi-Normal Modes from Bound States: The Numerical Approach
• Massless Dirac Perturbations of black holes in f(Q) gravity: quasinormal modes and weak deflection angle
• An Effective Model for the Quantum Schwarzschild Black Hole: Weak Deflection Angle, Quasinormal Modes and Bounding of Greybody Factor
• Charged black holes in Kalb-Ramond gravity: Weak Deflection Angle, Shadow cast, Quasinormal Modes and Neutrino annihilation
• Eikonal quasinormal modes, photon sphere and shadow of a charged black hole in the 4D Einstein-Gauss-Bonnet gravity
• Bound States of the Schwarzschild Black Hole
• An analytic approach to quasinormal modes for coupled linear systems
• Quasinormal mode and stability of optical black holes in moving dielectrics
• Scalar tachyonic instabilities in gravitational backgrounds: Existence and growth rate
• A new (original) set of Quasi-normal modes in spherically symmetric AdS black hole spacetimes
• Scattering of axial gravitational wave pulses by monopole black holes and QNMs
• Black hole physics within $f(R)$ gravity: Quasi-normal spectra and greybody factors
• New Results for Quasi Normal Modes of Gravitational Waves
• Nonperturbative Formulation of Resonances in Quantum Mechanics Based on Exact WKB Method
• Exact WKB method for radial Schrödinger equation
• Notes on Quasinormal Modes of charged de Sitter Blackholes from Quiver Gauge Theories
• Ringdown of a black hole sourced by a Burkert-density effective anisotropic source
• Quasinormal modes and the analytical continuation of non-self-adjoint operators
• Spectral Problems for Quasinormal Modes of Black Holes
• Quasinormal Modes of Black holes in the generalized Schwarzschild-de Sitter solution of $f(R)$ gravity
• Reissner-Nordström black holes in de Sitter space-time: bounds with quasinormal frequencies
• Gravitational Bound State Perturbations Inside Black Holes and Isospectrality
• Quasinormal Modes of Extremal Reissner-Nordstrom Black Holes via Seiberg-Witten Quantization