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The prediction of the spin of the black hole resulting from the merger of ageneric black-hole binary system is of great importance to study thecosmological evolution of supermassive black holes. Several attempts have beenrecently made to model the spin via simple expressions exploiting the resultsof numerical-relativity simulations. Here, I first review the derivation of aformula, proposed in Barausse & Rezzolla, Apj 704 L40, which accuratelypredicts the final spin magnitude and direction when applied to binaries withseparations of hundred or thousands of gravitational radii. This makes myformula particularly suitable for cosmological merger-trees and N-bodysimulations, which provide the spins and angular momentum of the two blackholes when their separation is of thousands of gravitational radii. Moreimportantly, I investigate the physical reason behind the good agreementbetween my formula and numerical relativity simulations, and nail it down tothe fact that my formula takes into account the post-Newtonian precession ofthe spins and angular momentum in a consistent manner.

The importance of precession in modelling the direction of the final spin from a black-hole merger