**Authors**: Ryuichi Fujita

**Date**: 29 Apr 2011

**Abstract**: We derive gravitational waveforms needed to compute the 14th post-Newtonian (14PN) order energy flux, i.e. $vˆ{28}$ beyond Newtonian approximation where $v$ is the orbital velocity of a test particle, in a circular orbit around a Schwarzschild black hole. We exhibit clearly the convergence of the energy flux in the PN expansion and suggest the fitting formula which can be used for more general case. The phase difference between the 14PN waveforms and numerical waveforms after two years inspiral becomes about $10ˆ{-7}$ for $\mu/M=10ˆ{-4}$ and $10ˆ{-3}$ for $\mu/M=10ˆ{-5}$ where $\mu$ and $M$ are the masses of a compact object and a supermassive black hole at the centers of galaxies respectively. The 14PN expressions will lead to the parameter estimation comparable to numerical waveforms for extreme mass ratio inspirals, which are one of the main targets of Laser Interferometer Space Antenna.

1104.5615
(/preprints)

2011-05-02, 13:56
**[edit]**

© M. Vallisneri 2012 — last modified on 2010/01/29

*Tantum in modicis, quantum in maximis*