Higher order WKB formula for quasinormal modes and grey-body factors: recipes for quick and accurate calculations
read the original abstract
The WKB approach for finding quasinormal modes of black holes, suggested in [1] by Schutz and Will at the first order and later developed to higher orders [2-4], became popular during the past decades, because, unlike more sophisticated numerical approaches, it is automatic for different effective potentials and mostly provides sufficient accuracy. At the same time, the seeming simplicity of the WKB approach resulted in appearance of a big number of partially misleading papers, where the WKB formula was used beyond its scope of applicability. Here we review various situations in which the WKB formula can or cannot bring us to reliable conclusions. As the WKB series converges only asymptotically, there is no mathematically strict criterium for evaluation of an error. Therefore, here we are trying to introduce a number of practical recipes instead and summarize cases in which higher WKB orders improve accuracy. We show that averaging of the Pade approximations, suggested first by J. Matyjasek and M. Opala [4], leads to much higher accuracy of the WKB approach, estimate the error and present the automatic code [5] which computes quasinormal modes and grey-body factors.
This paper has not been read by Pith yet.
Forward citations
Cited by 24 Pith papers
-
Testing Dark Energy with Black Hole Ringdown
Dynamical dark energy imprints O(1) shifts on black hole quasi-normal modes via cosmological hair, enabling constraints at 10^{-2} (LVK) to 10^{-4} (LISA) precision using the cubic Galileon as example.
-
Massive Scalar Quasinormal Modes, Greybody Factors, and Absorption Cross Section of a Parity-Symmetric Beyond-Horndeski Black Hole
Increasing the mass of a scalar field around a parity-symmetric beyond-Horndeski black hole strongly reduces the damping rate of quasinormal modes while suppressing low-frequency absorption and shifting efficient abso...
-
Eikonal quasinormal modes, greybody factors and shadow of charged accelerating black holes
Eikonal quasinormal modes for accelerating black holes are determined by the angular velocity and Lyapunov exponent of null geodesics, yielding universal greybody factors for any spin and explicit shadow radii that re...
-
Anomalous Decay Rate and Greybody Factors for Regular Black Holes with Scalar Hair
Regular black holes with scalar hair exhibit anomalous decay rates for massive scalar perturbations, with longest-lived modes switching to lower angular momentum above a critical mass.
-
Two types of quasinormal modes of Casadio-Fabbri-Mazzacurati brane-world black holes
Quasinormal modes of massive scalars in CFM brane-world black holes split into two types, with modes disappearing at critical masses where real or imaginary frequency parts reach zero.
-
Correspondence between quasinormal modes and grey-body factors of Schwarzschild--Tangherlini black holes
Quasinormal modes correspond well to grey-body factors for vector and tensor perturbations of Schwarzschild-Tangherlini black holes in all dimensions, but fail for scalar l=2 modes in D≥7 because of multiple potential...
-
Quasinormal modes of rotating black holes beyond general relativity in the WKB approximation
Higher-order WKB accurately computes quasinormal mode frequencies for rotating black holes beyond general relativity, with errors below current GW measurement precision for GW250114.
-
Long-lived massive scalar modes, grey-body factors, and absorption cross sections of the Reissner--Nordstr\"om-like brane-world black hole
Positive tidal charge in this brane-world black hole lowers the effective potential barrier, pushes massive scalar quasinormal modes toward arbitrarily long lifetimes, and increases transmission and absorption.
-
Scattering of electromagnetic field in quasi-topological gravity
Regular black holes in quasi-topological gravity produce shifted electromagnetic absorption spectra and modified photon sphere radii relative to singular Tangherlini solutions, with deviations suppressed as spacetime ...
-
Regular Black Holes in General Relativity from Nonlinear Electrodynamics with de Sitter Cores
New regular black hole metrics in GR arise from a magnetic monopole NLED configuration with de Sitter cores, are fitted to Sgr A* shadow size, and remain stable under scalar perturbations.
-
From Ringdown to Lensing: Analytic Eikonal Modes of Quasi-Topological Regular Black Holes
Analytic quasinormal-mode expressions and explicit QNM-shadow-lensing correspondence for four-dimensional quasi-topological regular black holes.
-
Quasi-resonances in the vicinity of Einstein-Maxwell-dilaton black hole
Increasing the mass of a perturbing scalar field around Einstein-Maxwell-dilaton black holes strongly suppresses damping in several quasinormal branches, producing quasi-resonant long-lived oscillations.
-
Axial gravitational perturbations and echo-like signals of a hairy black hole from gravitational decoupling
Axial perturbations around a hairy black hole from gravitational decoupling produce echo-like gravitational-wave signals that arise dynamically from a double-peak trapping cavity in the effective potential.
-
Long-lived quasinormal modes, shadows and particle motion in four-dimensional quasi-topological gravity
Massive scalar quasinormal modes in quasi-topological black holes become long-lived as scalar mass grows, while photon-sphere radius, shadow size, and ISCO exhibit moderate deviations from Schwarzschild.
-
Quasinormal mode/grey-body factor correspondence for Kerr black holes
WKB analysis of the Teukolsky equation establishes a quasinormal-mode to greybody-factor correspondence for Kerr black holes that holds in the eikonal limit for gravitational perturbations and matches numerics at high...
-
Quantum dust cores of black holes and their quasi-normal modes
Reviews quantum dust core black hole model with linear Misner-Sharp-Hernandez mass function and computes its quasi-normal modes, showing deviations from Schwarzschild sensitive to core surface quantum properties.
-
Scattering of scalar, electromagnetic, and Dirac fields in an asymptotically flat regular black hole supported by primordial dark matter
Raising the regularity parameter in this regular black-hole spacetime lowers the single-barrier potentials for all three fields, shifts transmission to lower frequencies, increases absorption cross sections, and produ...
-
Massive scalar quasinormal modes of an asymptotically flat regular black hole supported by a phantom Dirac--Born--Infeld field
Massive scalar quasinormal modes in this DBI-supported regular black hole show higher oscillation frequencies and lower damping as field mass increases, with larger regularity scales producing softer and longer-lived ringing.
-
A First-Order Eikonal Framework for Quasinormal Modes, Shadows, Strong Lensing, and Grey-Body Factors in a Scalarized Black-Hole Metric
Derives closed first-order eikonal expressions that connect a scalarized black-hole metric to quasinormal frequencies, shadows, strong deflection, and transmission probabilities.
-
A First-Order Eikonal Framework for Quasinormal Modes, Shadows, Strong Lensing, and Grey-Body Factors in a Scalarized Black-Hole Metric
First-order eikonal formulas connect a scalarized black-hole metric to quasinormal modes, shadows, strong lensing, and grey-body factors via photon-sphere invariants in the weak-hair limit.
-
Parametrized quasinormal modes, greybody factors and their correspondence
In the parametrized quasinormal mode framework, QNMs and GBFs depend on the order and polynomial power of potential modifications, with the QNM-GBF correspondence valid only in limited regimes.
-
Telling tails and quasi-resonances in the vicinity of Dymnikova regular black hole
Massive scalar perturbations on the Dymnikova regular black hole exhibit growing oscillation frequencies, reduced damping rates leading to quasi-resonances, power-law oscillatory tails, and mass-dependent suppression ...
-
The quasinormal modes of the rotating quantum corrected black holes
The work calculates scalar quasinormal mode spectra for a rotating quantum-corrected black hole and constructs a methodological pipeline to infer the quantum correction parameter from gravitational-wave ringdown data ...
-
Quasinormal modes and grey-body factors of axial gravitational perturbations of regular black holes in asymptotically safe gravity
Axial quasinormal modes of regular black holes in asymptotically safe gravity are weakly affected by the deviation parameter for the fundamental mode but show notable deviations for higher overtones, with strong agree...
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.