Bayesian analysis finds individual QNM frequencies near avoided crossings hard to resolve even under optimistic conditions, though collective AC waveform signatures may remain detectable if those modes dominate and slower-mode contamination is minimal.
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Exceptional Points and Resonance in Black Hole Ringdown
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abstract
We propose an exceptional-point (EP) framework for black-hole ringdown beyond the standard quasinormal-mode (QNM) paradigm. It provides a first-principles characterization of the resonance associated with avoided crossings near EPs, an effect that conventional QNM analysis cannot fully capture. Employing a phenomenological environmental black-hole model with the hyperboloidal framework, we identify near-coalescence of both QNM eigenvalues and eigenfunctions, and directly demonstrate that the resonance produces enhanced mode contributions in the time domain, resulting in characteristic departures from exponentially damped oscillations. Our formulation further reveals that the EP frequency, given by the average of the resonant modes, emerges as the physically relevant observable in the near-EP regime, and offers a robust foundation for modeling and extracting resonant ringdown signals.
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Homogeneous solutions and connection coefficients in the radial Teukolsky equation for Kerr black holes exhibit simple poles at Matsubara frequencies that cancel in the Green's function, along with canceling zero-frequency singularities scaling as ω^{-2l-1}.
Bilinear products for black hole quasinormal modes on hyperboloidal foliations are divergent due to CPT transformations but can be regularized to define orthogonal modes and excitation coefficients.
Complex scaling unifies quasinormal modes and continuum response for black-hole perturbations in four-dimensional Schwarzschild-de Sitter spacetimes.
A centered first-jet basis for neighboring quasinormal modes in finite time windows replaces the ill-conditioned sum of two resolved damped exponentials with a carrier plus t exp(-i omega_c t) term when the dimensionless splitting eta is small.
Complex scaling converts outgoing boundary conditions into eigenvalue problems to compute quasinormal frequencies for Schwarzschild and Reissner-Nordström black holes, including the extremal limit.
citing papers explorer
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Detectability of avoided crossings in black hole ringdowns
Bayesian analysis finds individual QNM frequencies near avoided crossings hard to resolve even under optimistic conditions, though collective AC waveform signatures may remain detectable if those modes dominate and slower-mode contamination is minimal.
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Pole Structure of Kerr Green's Function
Homogeneous solutions and connection coefficients in the radial Teukolsky equation for Kerr black holes exhibit simple poles at Matsubara frequencies that cancel in the Green's function, along with canceling zero-frequency singularities scaling as ω^{-2l-1}.
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Bilinear products and the orthogonality of quasinormal modes on hyperboloidal foliations
Bilinear products for black hole quasinormal modes on hyperboloidal foliations are divergent due to CPT transformations but can be regularized to define orthogonal modes and excitation coefficients.
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Quasinormal modes and continuum response of de Sitter black holes via complex scaling method
Complex scaling unifies quasinormal modes and continuum response for black-hole perturbations in four-dimensional Schwarzschild-de Sitter spacetimes.
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Finite-Window Centered Organization of Neighboring Poles
A centered first-jet basis for neighboring quasinormal modes in finite time windows replaces the ill-conditioned sum of two resolved damped exponentials with a carrier plus t exp(-i omega_c t) term when the dimensionless splitting eta is small.
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Complex scaling approach to quasinormal modes of Schwarzschild and Reissner--Nordstr\"om black holes
Complex scaling converts outgoing boundary conditions into eigenvalue problems to compute quasinormal frequencies for Schwarzschild and Reissner-Nordström black holes, including the extremal limit.
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