Resonance in black hole ringdown: Benchmarking quasinormal mode excitation and extraction

Abstract

We investigate how resonant excitation near exceptional points manifests in Kerr black hole ringdown waveforms and examine its extraction. Using waveforms generated by localized initial data, where quasinormal mode amplitudes are given solely by excitation factors, we establish a controlled benchmark for overtone extraction. Applying an iterative fitting method with mirror modes, we analyze a mild resonance in the $(l,m)=(2,2)$ multipole and a sharp resonance in the $(3,1)$ multipole occurring as part of a sequence of successive resonances. For $(2,2)$, we extract the fundamental mode, the first three overtones, and the fundamental mirror mode with relative errors below $10\%$, and show that residual waveforms exhibit the expected damped sinusoids together with distinctive resonance signatures. For $(3,1)$, we demonstrate that resonances can not only amplify but also reduce quasinormal mode excitations, reshaping the overtone hierarchy and rendering the sharp resonance more pronounced in ringdown. Our results clarify the imprint of resonance in Kerr ringdown and highlight both the robustness and limitations of current extraction techniques, providing a foundation for more reliable extraction of higher overtones and for applications to observational data analysis.

21 pages, 12 figures, dataset available at https://doi.org/10.5281/zenodo.18511200, matches published version

References in corpus (24)

• Non-Hermitian Physics
• Quasinormal ringing of Kerr black holes: The excitation factors
• Agnostic black hole spectroscopy: Quasinormal mode content of numerical relativity waveforms and limits of validity of linear perturbation theory
• Gravitational perturbations of the Kerr geometry: High-accuracy study
• Extracting linear and nonlinear quasinormal modes from black hole merger simulations
• Quasinormal-mode filters: a new approach to analyze the gravitational-wave ringdown of binary black-hole mergers
• Importance of mirror modes in binary black hole ringdown waveform
• Role of black hole quasinormal mode overtones for ringdown analysis
• Aspects of multimode Kerr ring-down fitting
• Black hole spectroscopy by mode cleaning
• Modelling the Ringdown from Precessing Black Hole Binaries
• Challenges testing the no-hair theorem with gravitational waves
• Challenges in Quasinormal Mode Extraction: Perspectives from Numerical solutions to the Teukolsky Equation
• Resonant Excitation of Quasinormal Modes of Black Holes
• Quasinormal modes of Schwarzschild black holes on the real axis
• Overtones and Nonlinearities in Binary Black Hole Ringdowns
• Striking the right tone: toward a self-consistent framework for measuring black hole ringdowns
• Quasinormal modes and excitation factors of Kerr black holes
• Iterative extraction of overtones from black hole ringdown
• Dynamical quasinormal mode excitation
• Recipes for computing radiation from a Kerr black hole using a generalized Sasaki-Nakamura formalism: Homogeneous solutions
• Black hole quasinormal mode resonances
• Robustness of extracting quasinormal mode information from black hole merger simulations
• Analyzing black-hole ringdowns with orthonormal modes

Cited by in corpus (3)

• Exact WKB method for radial Schrödinger equation
• Exceptional Lines and Excitation of (Nearly) Double-Pole Quasinormal Modes: A Semi-Analytic Study in the Nariai Black Hole
• Parity violating spectral dynamics of black holes in dynamical Chern-Simons gravity