  Building initial conditions for generic binary black-hole evolutions without
initial spurious eccentricity remains a challenge for numerical-relativity
simulations. This problem can be overcome by applying an eccentricity-removal
procedure which consists in evolving the binary for a couple of orbits,
estimating the eccentricity, and then correcting the initial conditions. The
presence of spins can complicate this procedure. As predicted by post-Newtonian
theory, spin-spin interactions and precession prevent the binary from moving
along an adiabatic sequence of spherical orbits, inducing oscillations in the
radial separation and in the orbital frequency. However, spin-induced
oscillations occur at approximately twice the orbital frequency, therefore they
can be distinguished from the initial spurious eccentricity, which occurs at
approximately the orbital frequency. We develop a new removal procedure based
on the derivative of the orbital frequency and find that it is successful in
reducing the eccentricity measured in the orbital frequency to less than 0.0001
when moderate spins are present. We test this new procedure using
numerical-relativity simulations of binary black holes with mass ratios 1.5 and
3, spin magnitude 0.5 and various spin orientations. The numerical simulations
exhibit spin-induced oscillations in the dynamics at approximately twice the
orbital frequency. Oscillations of similar frequency are also visible in the
gravitational-wave phase and frequency of the dominant mode.

General Relativity and Quantum Cosmology