Predicting the direction of the final spin from the coalescence of two
  black holes
  Knowledge of the spin of the black hole resulting from the merger of a
generic black-hole binary is of great importance for studying the cosmological
evolution of supermassive black holes. Several attempts have been made to model
the spin via simple expressions exploiting the results of numerical-relativity
simulations. While these expressions are in reasonable agreement with the
simulations, they neglect the precession of the binary's orbital plane, and
cannot therefore be applied directly -- i.e., without evolving the system to
small separations using post-Newtonian theory -- to binaries with separations
larger than a few hundred gravitational radii. While not a problem in
principle, this may be impractical if the formulas are employed in cosmological
merger-trees or N-body simulations, which provide the spins and angular
momentum of the two black holes when their separation is of hundreds or
thousands of gravitational radii. The formula that we propose is instead built
on improved assumptions and gives, for any separation, a very accurate
prediction both for the norm of the final spin and for its direction. By
comparing with the numerical data, we also show that the final-spin direction
is very accurately aligned with the binary's total angular momentum at large
separation. Hence, observations of the final-spin direction (e.g. via a jet)
can provide information on the binary's orbital plane at large separations and
could be relevant, for instance, for studying X-shaped radio sources.
