Exploring the Outer Limits of Numerical Relativity
  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=100M for three different resolutions.
We find that the orbital period of this binary (in the numerical coordinates)
is T=6422M. 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=20M, D=50M, and D=100M for
~ 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.
