Statistical studies of Spinning Black-Hole Binaries
  We study the statistical distributions of the spins of generic black-hole
binaries during the inspiral and merger, as well as the distributions of the
remnant mass, spin, and recoil velocity. For the inspiral regime, we start with
a random uniform distribution of spin directions S1 and S2 and magnitudes
S1=S2=0.97 for different mass ratios. Starting from a fiducial initial
separation of ri=50m, we perform 3.5PN evolutions down to rf=5m. At this final
fiducial separation, we compute the angular distribution of the spins with
respect to the final orbital angular momentum, L. We perform 16^4 simulations
for six mass ratios between q=1 and q=1/16 and compute the distribution of the
angles between L and Delta and L and S, directly related to recoil velocities
and total angular momentum. We find a small but statistically significant bias
of the distribution towards counter-alignment of both scalar products. To study
the merger of black-hole binaries, we turn to full numerical techniques. We
introduce empirical formulae to describe the final remnant black hole mass,
spin, and recoil velocity for merging black-hole binaries with arbitrary mass
ratios and spins. We then evaluate those formulae for randomly chosen
directions of the individual spins and magnitudes as well as the binary's mass
ratio. We found that the magnitude of the recoil velocity distribution decays
as P(v) \exp(-v/2500km/s), <v>=630km/s, and sqrt{<v^2> - <v>^2}= 534km/s,
leading to a 23% probability of recoils larger than 1000km/s, and a highly
peaked angular distribution along the final orbital axis. The final black-hole
spin magnitude show a universal distribution highly peaked at Sf/mf^2=0.73 and
a 25 degrees misalignment with respect to the final orbital angular momentum.
