(ed.). Gravitational waves (IOP, 2001)(422s).

356 Post-Newtonian computation of binary inspiral waveformsand s i = sin i where i is the inclination angle. The basic phase variable ψ enteringthe waveforms is defined byψ = φ − 2Gmω ( ) ωc 3 ln , (17.86)ω 0where φ is the actual orbital phase of the binary, and where ω 0 can be chosen asthe seismic cut-off of the detector (see [33] for details). As for the phase evolutionφ(t), it is given up to 2.5PN order, generalizing the Newtonian formula (17.52),byφ(t) = φ 0 − 1 { ( 3715τ 5/8 +ν 8064 + 55 )96 ν τ 3/8 − 3 4 πτ1/4( 9 275 495 284 875++14 450 688 258 048 ν + 1855 )2048 ν2 τ 1/8(38 645+ −172 032 − 15 ) }2048 ν π ln τ , (17.87)where φ 0 is a constant and where we recall that the dimensionless time variableτ was given by (17.50). The frequency is equal to the time derivative of (17.87),hencec3{ ( 743τ −3/8 +ω(t) =8Gm( 1 855 099+14 450 688+2688 + 1132 ν )τ −5/8 − 3 10 πτ−3/4+56 975258 048 ν + 3712048 ν2 )τ −7/8(− 772921 504 − 3256 ν )πτ −1 }. (17.88)We have checked that both waveforms (17.76)–(17.81) and phase/frequency(17.87)–(17.88) agree in the test mass limit ν → 0 with the results of linearblack hole perturbations as given by Tagoshi and Sasaki [34].References[1] Ciufolini I and Fidecaro F (ed) 1996 Gravitational Waves, Sources and Detectors(Singapore: World Scientific)[2] Marck J-A and Lasota J-P (ed) 1997 Relativistic Gravitation and GravitationalRadiation (Cambridge: Cambridge University Press)[3] Davier M and Hello P (ed) 1997 Gravitational Wave Data Analysis (Gif-sur-Yvette:Edition Frontières)[4] Will C M 1994 Proc. 8th Nishinomiya–Yukawa Symposium on RelativisticCosmology ed M Sasaki (Universal Academic)[5] Blanchet L 1997 Relativistic Gravitation and Gravitational Radiation ed J-A Marckand J-P Lasota (Cambridge: Cambridge Univerity Press)