An exceptional-point framework for black-hole ringdown characterizes resonances near avoided crossings, demonstrates enhanced mode contributions in the time domain, and identifies the EP frequency as the physically relevant observable.
Canonical reference
Overdamped modes in Schwarzschild-de Sitter and a Mathematica package for the numerical computation of quasinormal modes
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abstract
We present a package for Mathematica that facilitates the numerical computation of the quasinormal mode (QNM) spectrum of a black hole/black brane. Requiring as input only the QNM equation(s), the application of a single Mathematica function will compute the spectrum efficiently, by discretizing the equation(s) and solving the resulting generalized eigenvalue equation. It is applicable to a large variety of black holes, independent of their asymptotics. The package comes fully documented and with several tutorials. Here we present a self-contained review of the method and consider several applications. We illustrate the method in the simplest case of scalar QNMs of a Schwarzschild black brane in anti-de Sitter. Then we go on to look at the scalar QNMs of the Schwarzschild black hole in de Sitter, in anti-de Sitter and in asymptotically flat spacetimes, finding a novel infinite set of purely imaginary modes in the first case. We also derive the QNM equations for a generic Einstein-Maxwell-scalar background and use these to compute the QNMs of the asymptotically anti-de Sitter Reissner-Nordstr\"{o}m black brane, as a further illustration and check of the method.
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representative citing papers
Finite-temperature quasinormal modes in SYK connect infinite-T Christmas-tree spectra to JT gravity and show monotonic relaxation-rate growth only at strong coupling.
Analytic charged black holes in nonlinear electrodynamics with non-monotonic lapse functions support stable light rings and additional longer-lived quasinormal modes compared to Einstein gravity.
Semi-holographic systems with perturbative and holographic sectors exhibit prethermal time crystals through dissipationless modes in hydrodynamic channels plus short-wavelength instabilities that produce inhomogeneities over a wide temperature range.
Quasinormal frequencies for massless fields in Proca-hairy de Sitter black holes show scalar ℓ=0 modes most sensitive to hair parameter Q, with damping weakening near the three-horizon regime.
Axial perturbations of a gravitationally decoupled hairy black hole develop a double-peak potential that dynamically generates echo-like late-time waveforms in a suitable (α, β) region.
Numerical scattering calculations for neutral scalar and Dirac fields on Einstein-Euler-Heisenberg-de Sitter black holes show that Euler-Heisenberg coupling raises barriers and shifts transmission frequencies upward while cosmological constant lowers thresholds, with luminosity highly sensitive to t
Admissible negative-w_r branches of trace-quadratic f(R,T) black holes support axial ringdown spectra governed by a single master equation equivalent to Einstein gravity plus frozen anisotropic fluid, differing from Schwarzschild by ~22% with no resolved α dependence.
Applies sixth-order WKB to compute grey-body factors for test fields on generalized Proca black holes with effective de Sitter scale, finding that scalar mass and couplings raise barriers, suppress low-frequency transmission, and affect thermodynamics.
Massive scalar perturbations of de Sitter black holes in generalized Proca theory enter a large-mass regime with linearly growing real frequencies and constant damping rates, without true quasi-resonances, plus an analytic formula and shifts due to black-hole size and Proca hair.
Charged qOS black holes undergo Gauss-Bonnet scalarization in two regimes, producing linearly stable scalarized solutions for specific ranges of the action parameter α and coupling λ.
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 using informative priors.
Numerical spectra of total transmission modes in the draining bathtub model with vorticity can have positive or negative imaginary parts depending on parameters, with higher overtones exhibiting pronounced spectral mobility.
citing papers explorer
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Exceptional Points and Resonance in Black Hole Ringdown
An exceptional-point framework for black-hole ringdown characterizes resonances near avoided crossings, demonstrates enhanced mode contributions in the time domain, and identifies the EP frequency as the physically relevant observable.
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On the temperature dependence of quasinormal modes in SYK and holography
Finite-temperature quasinormal modes in SYK connect infinite-T Christmas-tree spectra to JT gravity and show monotonic relaxation-rate growth only at strong coupling.
-
Properties of black holes in non-linear electrodynamics
Analytic charged black holes in nonlinear electrodynamics with non-monotonic lapse functions support stable light rings and additional longer-lived quasinormal modes compared to Einstein gravity.
-
On prethermal time crystals from semi-holography
Semi-holographic systems with perturbative and holographic sectors exhibit prethermal time crystals through dissipationless modes in hydrodynamic channels plus short-wavelength instabilities that produce inhomogeneities over a wide temperature range.
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Quasinormal Spectra of Fields of Various Spin in Asymptotically de Sitter Black Holes within Generalized Proca Theory
Quasinormal frequencies for massless fields in Proca-hairy de Sitter black holes show scalar ℓ=0 modes most sensitive to hair parameter Q, with damping weakening near the three-horizon regime.
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Echoes of a hairy black hole from gravitational decoupling
Axial perturbations of a gravitationally decoupled hairy black hole develop a double-peak potential that dynamically generates echo-like late-time waveforms in a suitable (α, β) region.
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Scattering and Hawking Radiation from Einstein--Euler--Heisenberg--de Sitter Black Holes
Numerical scattering calculations for neutral scalar and Dirac fields on Einstein-Euler-Heisenberg-de Sitter black holes show that Euler-Heisenberg coupling raises barriers and shifts transmission frequencies upward while cosmological constant lowers thresholds, with luminosity highly sensitive to t
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Odd-parity perturbations of trace-quadratic $f(R,T)$ black holes with anisotropic matter: admissible branches, axial ringdown, and a coupled-PINN benchmark
Admissible negative-w_r branches of trace-quadratic f(R,T) black holes support axial ringdown spectra governed by a single master equation equivalent to Einstein gravity plus frozen anisotropic fluid, differing from Schwarzschild by ~22% with no resolved α dependence.
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Grey-Body Factors and Thermodynamics of Asymptotically de Sitter Black Holes in Generalized Proca Theory
Applies sixth-order WKB to compute grey-body factors for test fields on generalized Proca black holes with effective de Sitter scale, finding that scalar mass and couplings raise barriers, suppress low-frequency transmission, and affect thermodynamics.
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Long-lived quasinormal modes of Asymptotically de Sitter Black Holes in Generalized Proca Theory
Massive scalar perturbations of de Sitter black holes in generalized Proca theory enter a large-mass regime with linearly growing real frequencies and constant damping rates, without true quasi-resonances, plus an analytic formula and shifts due to black-hole size and Proca hair.
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Gauss-Bonnet scalarization of charged qOS-black holes
Charged qOS black holes undergo Gauss-Bonnet scalarization in two regimes, producing linearly stable scalarized solutions for specific ranges of the action parameter α and coupling λ.
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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 using informative priors.
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Total transmission modes in draining bathtub model with vorticity
Numerical spectra of total transmission modes in the draining bathtub model with vorticity can have positive or negative imaginary parts depending on parameters, with higher overtones exhibiting pronounced spectral mobility.