Gravitational waves from inclined orbits around Kerr black holes
Abstract
Extreme mass ratio inspirals on generic inclined orbits provide a critical dynamical probe of strong field gravity, as they uniquely break the severe parameter degeneracies inherent to planar equatorial trajectories. To isolate the exact rotational signatures, we extend the periodic-orbit framework to three-dimensional inclined trajectories in the Kerr spacetime, specifically focusing on the r--θ orbital resonances. By mapping the geodesic motion into a co-precessing spatial framework parameterized by Mino time, we compute the emitted quadrupole waveforms and evolve the local dynamics using circularity-preserving radiation reaction. It is demonstrated that frame-dragging induces a transient dynamical tilt at periastron, which directly splits the emitted radiation into an exact five-comb spectral architecture. When this resonant structure is resolved over a single coherence time, the statistical error on the dimensionless spin is reduced to σa ≈ 10−2, improving upon the equatorial baseline by up to two orders of magnitude. Because any bound orbit in a static, spherically symmetric spacetime generates a maximum of three frequency combs, the detection of this five-comb hierarchy establishes a rigorous, model-independent null test to strictly exclude spherical geometries.
Related
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BibTeX
@misc{huang2026gravitational,
title = {{Gravitational waves from inclined orbits around Kerr black holes}},
author = {Yi-Han Huang and Sen Guo and Yu Liang and Lin Wen and Kai Lin},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.31697},
eprint = {2610.31697},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.31697},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Gravitational waves from inclined orbits around Kerr black holes
AU - Yi-Han Huang
AU - Sen Guo
AU - Yu Liang
AU - Lin Wen
AU - Kai Lin
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.31697
UR - https://arxiv.org/abs/2610.31697
AB - Extreme mass ratio inspirals on generic inclined orbits provide a critical dynamical probe of strong field gravity, as they uniquely break the severe parameter degeneracies inherent to planar equatorial trajectories. To isolate the exact rotational signatures, we extend the periodic-orbit framework to three-dimensional inclined trajectories in the Kerr spacetime, specifically focusing on the r--θ orbital resonances. By mapping the geodesic motion into a co-precessing spatial framework parameterized by Mino time, we compute the emitted quadrupole waveforms and evolve the local dynamics using circularity-preserving radiation reaction. It is demonstrated that frame-dragging induces a transient dynamical tilt at periastron, which directly splits the emitted radiation into an exact five-comb spectral architecture. When this resonant structure is resolved over a single coherence time, the statistical error on the dimensionless spin is reduced to σ_a ≈ 10^−2, improving upon the equatorial baseline by up to two orders of magnitude. Because any bound orbit in a static, spherically symmetric spacetime generates a maximum of three frequency combs, the detection of this five-comb hierarchy establishes a rigorous, model-independent null test to strictly exclude spherical geometries.
ER -