Gespeichert in:
| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2511.06684 |
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Inhaltsangabe:
- 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.