Resonant bound orbits and kludge waveforms in rotating Konoplya-Zhidenko black hole spacetime
Abstract
We investigate timelike bound motion, resonant periodic orbits, and their gravitational-wave signatures in the rotating Konoplya-Zhidenko (KZ) black hole spacetime. Using the separability of the Hamilton-Jacobi equation, we parameterize eccentric and inclined bound orbits by (p,e,z1), derive the corresponding constants of motion (E,Lz,Q), and use the orbital frequencies to identify resonant configurations. We study a range of resonances, including radial-polar resonances of inclined orbits and radial-azimuthal resonances of equatorial eccentric orbits. We further construct physically scaled quadrupole-kludge waveforms for representative equatorial resonant orbits and analyze their frequency-domain characteristics. Our results show that the KZ deformation shifts the resonance locations and modifies both the orbital trajectories and the resulting gravitational-wave signals. The corresponding characteristic strain lies predominantly in the millihertz band, placing these signals in the frequency range relevant to space-based gravitational wave detectors.
Related
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BibTeX
@misc{dai2026resonant,
title = {{Resonant bound orbits and kludge waveforms in rotating Konoplya-Zhidenko black hole spacetime}},
author = {Qiyu Dai and Xiongjun Fang and Xiao-Mei Kuang and Jiliang Jing},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.29234},
eprint = {2608.29234},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.29234},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Resonant bound orbits and kludge waveforms in rotating Konoplya-Zhidenko black hole spacetime
AU - Qiyu Dai
AU - Xiongjun Fang
AU - Xiao-Mei Kuang
AU - Jiliang Jing
PY - 2026
DA - 2026/08/29
PB - arXiv
DO - 10.48550/arxiv.2608.29234
UR - https://arxiv.org/abs/2608.29234
AB - We investigate timelike bound motion, resonant periodic orbits, and their gravitational-wave signatures in the rotating Konoplya-Zhidenko (KZ) black hole spacetime. Using the separability of the Hamilton-Jacobi equation, we parameterize eccentric and inclined bound orbits by (p,e,z_1), derive the corresponding constants of motion (E,L_z,Q), and use the orbital frequencies to identify resonant configurations. We study a range of resonances, including radial-polar resonances of inclined orbits and radial-azimuthal resonances of equatorial eccentric orbits. We further construct physically scaled quadrupole-kludge waveforms for representative equatorial resonant orbits and analyze their frequency-domain characteristics. Our results show that the KZ deformation shifts the resonance locations and modifies both the orbital trajectories and the resulting gravitational-wave signals. The corresponding characteristic strain lies predominantly in the millihertz band, placing these signals in the frequency range relevant to space-based gravitational wave detectors.
ER -