The Bardeen-Petterson effect in accreting supermassive black-hole
  binaries: a systematic approach
  Disc-driven migration is a key evolutionary stage of supermassive black-hole
binaries hosted in gas-rich galaxies. Besides promoting the inspiral, viscous
interactions tend to align the spins of the black holes with the orbital
angular momentum of the disc. We present a critical and systematic
investigation of this problem, also known as the Bardeen-Petterson effect. We
design a new iterative scheme to solve the non-linear dynamics of warped
accretion discs under the influence of both relativistic frame dragging and
binary companion. We characterize the impact of the disc "critical obliquity",
which marks regions of the parameter space where stationary solutions do not
exist. We find that black-hole spins reach either complete alignment or a
critical configuration. Reaching the critical obliquity might imply that the
disc breaks as observed in hydrodynamical simulations. Our findings are
important to predict the spin configurations with which supermassive black-hole
binaries enter their gravitational-wave driven regime and become detectable by
LISA.
