On the equal-mass limit of precessing black-hole binaries
  We analyze the inspiral dynamics of equal-mass precessing black-hole binaries
using multi-timescale techniques. The orbit-averaged post-Newtonian
evolutionary equations admit two constants of motion in the equal-mass limit,
namely the magnitude of the total spin $S$ and the effective spin $\xi$. This
feature makes the entire dynamics qualitatively different compared to the
generic unequal-mass case, where only $\xi$ is constant while the variable $S$
parametrizes the precession dynamics. For fixed individual masses and spin
magnitudes, an equal-mass black-hole inspiral is uniquely characterized by the
two parameters $(S,\xi)$: these two numbers completely determine the entire
evolution under the effect of radiation reaction. In particular, for equal-mass
binaries we find that (i) the black-hole binary spin morphology is constant
throughout the inspiral, and that (ii) the precessional motion of the two
black-hole spins about the total spin takes place on a longer timescale than
the precession of the total spin and the orbital plane about the total angular
momentum.
