2025/11/10 by Zhang, Chen, Han, Wen-Biao
Engineering · Physics and Astronomy · #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geophysics and Sensor Technology #Pulsars and Gravitational Waves Research
paper · doi:10.48550/arxiv.2511.06684
openalex publication_date 2025/11/10 · openalex created_date 2025/11/12 · openalex updated_date 2026/07/28
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 Ωr, ~Ωθ, ~Ωϕ 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.