2011/04/30 by R. Fujita, Ryuichi Fujita
Physics and Astronomy · #Astrophysical Phenomena and Observations #Pulsars and Gravitational Waves Research #Relativity and Gravitational Theory #gr-qc
paper · pdf · doi:10.1143/ptp.127.583
published as Prog. Theor. Phys. 127 (2012), 583-590 · 8 pages, 2 figures
crossref issued 2012/03/01 · crossref published 2012/03/01 · crossref published-print 2012/03/01 · openalex publication_date 2012/03/01 · crossref created 2012/03/22 · arxiv created 2012/08/27 · arxiv updated 2012/08/28 · openalex created_date 2016/06/24 · crossref deposited 2019/06/25 · crossref indexed 2026/07/30 · openalex updated_date 2026/07/30
We derive gravitational waveforms needed to compute the 14th post-Newtonian (14PN) order energy flux for a particle in circular orbit around a Schwarzschild black hole, i.e. v28 beyond the leading Newtonian approximation where v is the orbital velocity of a test particle. We investigate the convergence of the energy flux in the PN expansion and suggest a fitting formula which can be used to extract unknown higher order PN coefficients from accurate numerical data for more general orbits around a Kerr black hole. The phase difference between the 14PN waveforms and numerical waveforms after two years inspiral is shown to be about 10-7 for μ/M=10-4 and 10-3 for μ/M=10-5 where μ is the mass of a compact object and M the mass of the central supermassive black hole. In first order black hole perturbation theory, for extreme mass ratio inspirals which are one of the main targets of Laser Interferometer Space Antenna, the 14PN expressions will lead to the data analysis accuracies comparable to the ones resulting from high precision numerical waveforms.