We perform several black-hole binary evolutions using fully nonlinear numerical relativity techniques at separations large enough that low-order post-Newtonian expansions are expected to be accurate .
As a case study , we evolve an equal-mass nonspinning black-hole binary from a quasicircular orbit at an initial coordinate separation of D = 100 M for three different resolutions .
We find that the orbital period of this binary ( in the numerical coordinates ) is T = 6422 M .
The orbital motion agrees with post-Newtonian predictions to within 1 \% .
Interestingly , we find that the time derivative of the coordinate separation is dominated by a purely gauge effect leading to an apparent contraction and expansion of the orbit at twice the orbital frequency .
Based on these results , we improved our evolution techniques and studied a set of black hole binaries in quasi-circular orbits starting at D = 20 M , D = 50 M , and D = 100 M for \sim 5 , 3 , and 2 orbits , respectively .
We find good agreement between the numerical results and post-Newtonian predictions for the orbital frequency and radial decay rate , radiated energy and angular momentum , and waveform amplitude and phases .
The results are relevant for the future computation of long-term waveforms to assist in the detection and analysis of gravitational waves by the next generation of detectors as well as the long-term simulations of black-hole binaries required to accurately model astrophysically realistic circumbinary accretion disks .