How much of the black hole ringdown is sourced within the light ring?

@misc{cheung2026much,
  title = {{How much of the black hole ringdown is sourced within the light ring?}},
  author = {Mark Ho-Yeuk Cheung},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.29466},
  eprint = {2608.29466},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.29466},
}

TY  - UNPB
TI  - How much of the black hole ringdown is sourced within the light ring?
AU  - Mark Ho-Yeuk Cheung
PY  - 2026
DA  - 2026/08/29
PB  - arXiv
DO  - 10.48550/arxiv.2608.29466
UR  - https://arxiv.org/abs/2608.29466
AB  - Not much. It has been proposed that applying a rational filter to a black hole ringdown gravitational waveform reveals a direct wave component sourced near the event horizon. By solving the Teukolsky equation for a point particle plunging into a Kerr black hole, I show that the maximum amplitude of the waves sourced within the prograde light ring is ≲ 10% that of those sourced by the full trajectory no matter if the waves are filtered or not. This agrees with the interpretation of quasinormal modes as waves orbiting the light ring and the direct wave as the power of these modes redistributed in time. Therefore, both quasinormal modes and direct waves are more a probe of the light ring than the near-horizon region. For GW250114, I estimate that the component of the waves sourced within the light ring have a signal-to-noise ratio ρ≲ 1 measured after the peak of the filtered waves.
ER  -