Comparison of Post-Newtonian and Numerical Evolutions of Black-Hole Binaries

In this paper, we compare the waveforms from the post-Newtonian (PN) approach with the numerical simulations of generic black-hole binaries which have mass ratio $q\sim 0.8$, arbitrarily oriented spins with magnitudes $S_1\mathrm{/}{m}_1^2\sim 0.6$ and $S_2\mathrm{/}{m}_2^2\sim 0.4$, and orbit 9 times from an initial orbital separation of $r\approx 11M$ prior to merger. We observe a reasonably good agreement between the PN and numerical waveforms, with an overlap of over 98% for the first six cycles of the $(\mathrm{\ell }=2,m=\pm 2)$ mode and over 90% for the $(\mathrm{\ell }=2,m=1)$ and $(\mathrm{\ell }=3,m=3)$ modes.