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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.06684 |
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| _version_ | 1866915608738660352 |
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| author | Zhang, Chen Han, Wen-Biao |
| author_facet | Zhang, Chen Han, Wen-Biao |
| contents | We derive the approximate analytical solutions of the bound timelike geodesic orbits in the effective-one-body (EOB) frame with extreme-mass ratio limit. The analytical solutions are expressed in terms of the elliptic integrals using Mino time $λ$ as the independent variable. Since Mino time decouples the $r$ and $θ$-motion, we also give explicit expressions for three orbital frequencies $Ω_r, ~Ω_θ, ~Ω_ϕ$ using the Fourier series expansion. With these analytical expressions at hand, we can perform Fourier expansions in Mino time $λ$ for any function expressed in terms of the coordinates $(r,θ,ϕ)$. In particular, the observer's time t is decomposed into Mino time $λ$, and the frequency-domain description is constructed from the $λ$-Fourier expansion and the expansion of t. These analytical expressions are quite simple to implement, and can be applicable for calculating gravitational waves (GWs) from extreme mass-ratio inspirals (EMRIs) with the frequency-domain Teukolsky equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_06684 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Analytical solutions of bound timelike geodesic orbits in effective-one-body frame Zhang, Chen Han, Wen-Biao General Relativity and Quantum Cosmology We derive the approximate analytical solutions of the bound timelike geodesic orbits in the effective-one-body (EOB) frame with extreme-mass ratio limit. The analytical solutions are expressed in terms of the elliptic integrals using Mino time $λ$ as the independent variable. Since Mino time decouples the $r$ and $θ$-motion, we also give explicit expressions for three orbital frequencies $Ω_r, ~Ω_θ, ~Ω_ϕ$ using the Fourier series expansion. With these analytical expressions at hand, we can perform Fourier expansions in Mino time $λ$ for any function expressed in terms of the coordinates $(r,θ,ϕ)$. In particular, the observer's time t is decomposed into Mino time $λ$, and the frequency-domain description is constructed from the $λ$-Fourier expansion and the expansion of t. These analytical expressions are quite simple to implement, and can be applicable for calculating gravitational waves (GWs) from extreme mass-ratio inspirals (EMRIs) with the frequency-domain Teukolsky equation. |
| title | Analytical solutions of bound timelike geodesic orbits in effective-one-body frame |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2511.06684 |