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| Natura: | Preprint |
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2025
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| Accesso online: | https://arxiv.org/abs/2511.14080 |
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| _version_ | 1866908946749456384 |
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| author | Zhang, Chao Zhu, Tao |
| author_facet | Zhang, Chao Zhu, Tao |
| contents | The $γ$-metric, also known as Zipoy-Voorhees spacetime, is a static, axially symmetric vacuum solution to Einstein's field equations characterized by two parameters: mass and the deformation parameter $γ$. It reduces to the Schwarzschild metric when $γ= 1$. In this paper, we explore potential signatures of the $γ$-metric on periodic orbits and their gravitational-wave radiation. Periodic orbits are classified by a rotational number specified by three topological numbers $(z, w, v)$, each triple corresponding to characteristic zoom-whirl behavior. We show that deviations from $γ=1$ alter the radii and angular momentum of bound orbits and thereby shift the $(z, w, v)$ taxonomy. We also compute representative gravitational waveforms for certain periodic orbits and demonstrate that $γ\neq 1$ can induce phase shifts and amplitude modulations correlated with changes in the zoom-whirl structure. In particular, larger zoom numbers lead to increasingly complex substructures in the waveforms, and finite deviations from $γ=1$ can significantly modify these features. Our results indicate that precise measurements of waveform morphology from extreme-mass-ratio inspirals may constrain deviations from spherical symmetry encoded in $γ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_14080 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Periodic orbits and their gravitational wave radiations in $γ$-metric Zhang, Chao Zhu, Tao General Relativity and Quantum Cosmology High Energy Physics - Theory The $γ$-metric, also known as Zipoy-Voorhees spacetime, is a static, axially symmetric vacuum solution to Einstein's field equations characterized by two parameters: mass and the deformation parameter $γ$. It reduces to the Schwarzschild metric when $γ= 1$. In this paper, we explore potential signatures of the $γ$-metric on periodic orbits and their gravitational-wave radiation. Periodic orbits are classified by a rotational number specified by three topological numbers $(z, w, v)$, each triple corresponding to characteristic zoom-whirl behavior. We show that deviations from $γ=1$ alter the radii and angular momentum of bound orbits and thereby shift the $(z, w, v)$ taxonomy. We also compute representative gravitational waveforms for certain periodic orbits and demonstrate that $γ\neq 1$ can induce phase shifts and amplitude modulations correlated with changes in the zoom-whirl structure. In particular, larger zoom numbers lead to increasingly complex substructures in the waveforms, and finite deviations from $γ=1$ can significantly modify these features. Our results indicate that precise measurements of waveform morphology from extreme-mass-ratio inspirals may constrain deviations from spherical symmetry encoded in $γ$. |
| title | Periodic orbits and their gravitational wave radiations in $γ$-metric |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2511.14080 |