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PreprintarXiv licencearXiv

Rational Orbits and Gravitational-Wave Signatures around a Horndeski Black Hole

  • Wei Gao
  • Xiaoyan Zhu
  • Wenbin Lin
  • Siming Liu
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Abstract

We study equatorial timelike geodesics and associated gravitational-wave (GW) emission for a static Horndeski black hole with secondary scalar hair, characterized by an effective pressure parameter peff. Using the rational-orbit taxonomy (z,w,v), we analyze the innermost stable circular orbit (ISCO), marginally bound orbit (MBO), and periodic bound orbits. We find that increasing peff systematically shifts orbital radii outward and modifies the rational parameter q. Within the test-particle and quadrupole approximations, we estimate GW signals from an extreme mass-ratio inspiral (EMRI) system at a luminosity distance of DL=8000 pc. The characteristic strains reach ∼10−18 in the mHz band, partially overlapping the nominal LISA sensitivity range. These results demonstrate that Horndeski corrections systematically alter strong-field orbital dynamics and GW spectra, offering a phenomenological probe of deviations from general relativity.

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Cite

BibTeXRIS
BibTeX
@misc{gao2026rational,
  title = {{Rational Orbits and Gravitational-Wave Signatures around a Horndeski Black Hole}},
  author = {Wei Gao and Xiaoyan Zhu and Wenbin Lin and Siming Liu},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.07596},
  eprint = {2611.07596},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.07596},
}
RIS
TY  - UNPB
TI  - Rational Orbits and Gravitational-Wave Signatures around a Horndeski Black Hole
AU  - Wei Gao
AU  - Xiaoyan Zhu
AU  - Wenbin Lin
AU  - Siming Liu
PY  - 2026
DA  - 2026/11/05
PB  - arXiv
DO  - 10.48550/arxiv.2611.07596
UR  - https://arxiv.org/abs/2611.07596
AB  - We study equatorial timelike geodesics and associated gravitational-wave (GW) emission for a static Horndeski black hole with secondary scalar hair, characterized by an effective pressure parameter p_eff. Using the rational-orbit taxonomy (z,w,v), we analyze the innermost stable circular orbit (ISCO), marginally bound orbit (MBO), and periodic bound orbits. We find that increasing p_eff systematically shifts orbital radii outward and modifies the rational parameter q. Within the test-particle and quadrupole approximations, we estimate GW signals from an extreme mass-ratio inspiral (EMRI) system at a luminosity distance of D_L=8000 pc. The characteristic strains reach ∼10^−18 in the mHz band, partially overlapping the nominal LISA sensitivity range. These results demonstrate that Horndeski corrections systematically alter strong-field orbital dynamics and GW spectra, offering a phenomenological probe of deviations from general relativity.
ER  -