Periodic Orbits and Their Gravitational-Wave Signatures around a Rotating Black Hole Surrounded by Perfect Fluid Dark Matter
Abstract
We investigate equatorial timelike motion of a massive test particle and the associated gravitational radiation around a Kerr black hole surrounded by perfect fluid dark matter. In the presence of a dark matter fluid, the radius of the innermost stable circular orbit decreases, while the specific angular momentum is modified and the specific energy increases as the dark matter (DM) parameter, α, increases. We compute periodic timelike orbits using the rational frequency ratio q, with the (z,w,v) classification, which is modified by the presence of DM while preserving the topological class. We analyze the gravitational waveforms corresponding to these periodic orbits and find that dark matter modifies the timing and distribution of the oscillatory features of the orbits. For a representative extreme-mass-ratio system, the corresponding characteristic strain is concentrated mainly in the millihertz (mHz) frequency band relevant to LISA. These results establish a direct connection between the dark-matter-induced modifications of strong-field orbital dynamics and the corresponding gravitational-wave signatures.
Related
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BibTeX
@misc{shahzad2026periodic,
title = {{Periodic Orbits and Their Gravitational-Wave Signatures around a Rotating Black Hole Surrounded by Perfect Fluid Dark Matter}},
author = {M. R. Shahzad and Hamza Rehman and Saddam Hussain and Tao Zhu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.07020},
eprint = {2610.07020},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.07020},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Periodic Orbits and Their Gravitational-Wave Signatures around a Rotating Black Hole Surrounded by Perfect Fluid Dark Matter
AU - M. R. Shahzad
AU - Hamza Rehman
AU - Saddam Hussain
AU - Tao Zhu
PY - 2026
DA - 2026/10/04
PB - arXiv
DO - 10.48550/arxiv.2610.07020
UR - https://arxiv.org/abs/2610.07020
AB - We investigate equatorial timelike motion of a massive test particle and the associated gravitational radiation around a Kerr black hole surrounded by perfect fluid dark matter. In the presence of a dark matter fluid, the radius of the innermost stable circular orbit decreases, while the specific angular momentum is modified and the specific energy increases as the dark matter (DM) parameter, α, increases. We compute periodic timelike orbits using the rational frequency ratio q, with the (z,w,v) classification, which is modified by the presence of DM while preserving the topological class. We analyze the gravitational waveforms corresponding to these periodic orbits and find that dark matter modifies the timing and distribution of the oscillatory features of the orbits. For a representative extreme-mass-ratio system, the corresponding characteristic strain is concentrated mainly in the millihertz (mHz) frequency band relevant to LISA. These results establish a direct connection between the dark-matter-induced modifications of strong-field orbital dynamics and the corresponding gravitational-wave signatures.
ER -