2011/03/29 by G. Koekoek, J.W. van Holten, J. W. van Holten · 1 citation
Mathematics · Physics and Astronomy · #Astrophysical Phenomena and Observations #Astrophysics #Black Holes and Theoretical Physics #Classical mechanics #General relativity #Geodesic #Gravitation #Gravitational wave #Mass ratio #Mathematical analysis #Mathematics #Physics #Pulsars and Gravitational Waves Research #Quantum mechanics #RADIUS #Schwarzschild metric #Schwarzschild radius #Solving the geodesic equations #Spacetime #gr-qc
paper · pdf · doi:10.1088/0264-9381/28/22/225022
published as Class. Quantum Grav. 28 (2011) 225022
arxiv created 2011/03/29 · openalex publication_date 2011/10/25 · arxiv updated 2015/11/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The method of geodesic deviations has been applied to derive accurate analytic approximations to geodesics in Schwarzschild spacetime. The results are used to construct analytic expressions for the source terms in the Regge–Wheeler and Zerilli–Moncrief equations, which describe the propagation of gravitational waves emitted by a compact massive object moving in the Schwarzschild background spacetime. The wave equations are solved numerically to provide the asymptotic form of the wave at large distances for a series of non-circular bound orbits with periastron distances up to the ISCO radius, and the power emitted in gravitational waves by the extreme mass-ratio binary system is computed. The results compare well with those of purely numerical approaches.