Direct waves in filtered Schwarzschild ringdown are the anti-causal filter-pole contribution sourced by near-horizon trajectory dynamics and do not vanish.
Prompt Response from Plunging Sources in Schwarzschild Spacetime
7 Pith papers cite this work. Polarity classification is still indexing.
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abstract
Gravitational waves generated by moving sources in Schwarzschild spacetime can be decomposed into three principal components: quasinormal modes, tail, and prompt response. While the first two have been extensively studied, a systematic and exact treatment of the prompt response has received comparatively little attention. In this work, building on recent progress in elucidating the structure of the Green's function of the Regge-Wheeler equation, we place the prompt response on a firm theoretical footing and investigate its morphology for sources inspiraling and plunging into a Schwarzschild black hole. We find that during the inspiral phase, the prompt response is stronger than the dynamical excitation of quasinormal modes by a factor of ~1.2, with both contributions modulated by the instantaneous orbital motion. Near the waveform peak, the prompt response rapidly decays, while the quasinormal modes transition into the ringdown regime. By combining the prompt response, quasinormal modes, and tail contributions, we achieve an accurate reconstruction of the full time-domain inspiral-merger-ringdown waveform at the 99$\%$ level, thereby providing strong support for the accuracy of this decomposition. These results offer new insight into the transition from inspiral to merger and ringdown.
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gr-qc 7years
2026 7representative citing papers
A bouncing singularity from a null geodesic sets the convergence of the QNM expansion for the Schwarzschild retarded Green's function.
Introduces Debye series and Debye-QNMs to decompose waveforms from Schwarzschild-star models, achieving early-time convergence and organizing ringdown plus echo packets into individual propagation channels.
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.
Refined propagation prescription for quasinormal modes excited by plunging particles confirms a bounce radius at r_*=0 and yields accurate reproduction of the post-bounce oscillatory waveform component from first principles.
Direct waves are identified in NR ringdown waveforms using QNM extraction techniques over a range of start times, but their frequency deviates from the horizon-mode prediction.
citing papers explorer
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Foundations of Direct Waves in Schwarzschild Ringdown
Direct waves in filtered Schwarzschild ringdown are the anti-causal filter-pole contribution sourced by near-horizon trajectory dynamics and do not vanish.
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Bouncing singularities in Schwarzschild: a geometric origin of the QNM convergence region
A bouncing singularity from a null geodesic sets the convergence of the QNM expansion for the Schwarzschild retarded Green's function.
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Ringdown and echoes from compact objects: Debye series and Debye quasinormal modes
Introduces Debye series and Debye-QNMs to decompose waveforms from Schwarzschild-star models, achieving early-time convergence and organizing ringdown plus echo packets into individual propagation channels.
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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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Dynamical quasinormal mode excitation II: propagation and convergence in Schwarzschild
Refined propagation prescription for quasinormal modes excited by plunging particles confirms a bounce radius at r_*=0 and yields accurate reproduction of the post-bounce oscillatory waveform component from first principles.
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Modeling Direct Waves in Binary Black Hole Ringdowns
Direct waves are identified in NR ringdown waveforms using QNM extraction techniques over a range of start times, but their frequency deviates from the horizon-mode prediction.
- Pole structure of the Kerr Green's function