Wide nutation: binary black-hole spins repeatedly oscillating from full alignment to full anti-alignment

Within the framework of 2PN black-hole binary spin precession, we explore configurations where one of the two spins oscillates from being completely aligned with the orbital angular momentum to being completely anti-aligned with it during a single precession cycle. This wide nutation is the extreme limit of the generic phenomenon of spin nutation in black-hole binaries. Crucially, wide nutation happens on the short precession time scale and it is not a secular effect due to gravitational-wave radiation reaction. The spins of these binaries, therefore, flip repeatedly as one of these special configurations is entered. Binaries with total mass M, mass ratio q, and dimensionless spin X1(X2) of the more (less) massive black hole are allowed to undergo wide nutation at binary separations r ≤ rwide ≡ [(qX2 - X1)/(1 - q)]2M. Sources that are more likely to nutate widely have similar masses and effective spins close to zero.