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Authors: Luciano Rezzolla, Peter Diener, Ernst Nils Dorband, Denis Pollney, Christian Reisswig, Erik Schnetter, Jennifer Seiler

Date: 17 Oct 2007

Abstract: Determining the final spin of a black-hole binary is a question of key importance in astrophysics, and it has attracted a renewed interest since numerical-relativity simulations have allowed the first quantitative measures. Modelling this quantity in general is made difficult by the fact that it depends on the 7-dimensional space of parameters characterizing the two initial black holes. However, in special cases, when symmetries can be exploited, the description can become considerably simpler. For black-hole binaries with unequal masses but with equal spins which are aligned with the orbital angular momentum, we show that the use of recent numerical-relativity simulations and basic but exact constraints inspired from the extreme mass-ratio limit allow to model this quantity with a simple analytic expression. Despite the simple dependence, the fitting expression models very accurately all of the available estimates, with errors of a couple of percent at most. We also discuss how to use the fitting function to predict when a Schwarzschild black hole is produced by the merger of two spinning black holes, when the spin of the spacetime ‘flips’ sign, or under what conditions the final black hole is ‘spun-up’ by the merger. Last but not least, we show that the fit obtained here can be trivially extended to consider unequal-spin binaries, thus providing a complete description of the final spin from the coalescence of generic black-hole binaries with spins aligned to the orbital angular momentum.

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