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PreprintarXiv licencearXiv

The Start Time of Ringdown

  • Adrien Kuntz
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Abstract

We determine the convergence of quasi-normal modes sums for a point-particle plunging into a Schwarzschild black hole. While a dynamical amplitude model reproduces the waveform after the particle crosses the bounce radius, a constant amplitude sum converges only after the start time tS, which corresponds to the advanced time at which the particle hits the central singularity. For a plunge from the ISCO, tS ≃ 9.4 M after the peak of the $22$ mode. After tS, dynamical and constant amplitudes models are equivalent; our analysis also implies that any "direct wave" must reduce to the late-time tail after tS.

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Cite

BibTeXRIS
BibTeX
@misc{kuntz2026start,
  title = {{The Start Time of Ringdown}},
  author = {Adrien Kuntz},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.05472},
  eprint = {2611.05472},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.05472},
}
RIS
TY  - UNPB
TI  - The Start Time of Ringdown
AU  - Adrien Kuntz
PY  - 2026
DA  - 2026/11/03
PB  - arXiv
DO  - 10.48550/arxiv.2611.05472
UR  - https://arxiv.org/abs/2611.05472
AB  - We determine the convergence of quasi-normal modes sums for a point-particle plunging into a Schwarzschild black hole. While a dynamical amplitude model reproduces the waveform after the particle crosses the bounce radius, a constant amplitude sum converges only after the start time t_S, which corresponds to the advanced time at which the particle hits the central singularity. For a plunge from the ISCO, t_S ≃ 9.4 M after the peak of the $22$ mode. After t_S, dynamical and constant amplitudes models are equivalent; our analysis also implies that any "direct wave" must reduce to the late-time tail after t_S.
ER  -