Estimating the final spin of a binary black hole coalescence

Abstract

We present a straightforward approach for estimating the final black hole spin of a binary black hole coalescence with arbitrary initial masses and spins. Making some simple assumptions, we estimate the final angular momentum to be the sum of the individual spins plus the orbital angular momentum of a test particle orbiting at the last stable orbit around a Kerr black hole with a spin parameter of the final black hole. The formula we obtain is able to reproduce with reasonable accuracy the results from available numerical simulations, but, more importantly, it can be used to investigate what configurations might give rise to interesting dynamics. In particular, we discuss scenarios which might give rise to a ``flip'' in the direction of the total angular momentum of the system. By studying the dependence of the final spin upon the mass ratio and initial spins we find that our simple approach suggests that it is not possible to spin-up a black hole to extremal values through merger scenarios irrespective of the mass ratio of the objects involved.

9 pages, 8 figures

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• Effective one body approach to the dynamics of two spinning black holes with next-to-leading order spin-orbit coupling
• The final mass and spin of black hole mergers
• Eccentric binary black-hole mergers: The transition from inspiral to plunge in general relativity
• Extra-Large Remnant Recoil Velocities and Spins from Near-Extremal-Bowen-York-Spin Black-Hole Binaries
• Binary black holes' effects on electromagnetic fields
• Perturbed disks get shocked. Binary black hole merger effects on accretion disks
• The spin expansion for binary black hole merger: new predictions and future directions
• Can binary mergers produce maximally spinning black holes?
• Multipolar analysis of spinning binaries
• Numerical Relativity meets Data Analysis: Spinning Binary Black Hole Case