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We compare waveforms and orbital dynamics from the first long-term, fully nonlinear, numerical simulations of a generic black-hole binary configuration with post-Newtonian (PN) predictions. The binary has mass ratio q0. 8 with arbitrarily oriented spins of magnitude S₁/m₁^20. 6 and S₂/m₂^20. 4 and orbits 9 times prior to merger. The numerical simulation starts with an initial separation of r11M and orbital parameters determined by 2. 5 PN and 3. 5 PN evolutions of a quasi-circular binary starting from r=50M. The resulting binaries have very little eccentricity according to the 2. 5 PN and 3. 5 PN systems, but show eccentricities of e0. 01--0. 02 and e0. 002--0. 005 in the respective numerical simulations, thus demonstrating that 3. 5 PN significantly reduces the eccentricity of the binary compared to 2. 5 PN. We perform three numerical evolutions from r11M with maximum resolutions of h=M/48, M/53. 3, M/59. 3, to verify numerical convergence. We observe a reasonably good agreement between the PN and numerical waveforms, with an overlap of nearly 99% for the first six cycles of the (=2, m=2) modes, 91% for the (=2, m=1) modes, and nearly 91% for the (=3, m=3) modes. The phase differences between numerical and post-Newtonian approximations appear to be independent of the (, m) modes considered and relatively small for the first 3--4 orbits. An advantage of the 3. 5 PN model over the 2. 5 PN one seems to be observed, which indicates that still higher PN order (perhaps even 4. 0 PN) may yield significantly better waveforms. In addition, we identify features in the waveforms likely related to precession and precession-induced eccentricity.
Campanelli et al. (Mon,) studied this question.