Estimating the final spin of a binary black hole coalescence

TL;DR

This paper introduces a simple, analytical method to estimate the final spin of a black hole resulting from a binary merger, aligning well with numerical simulations and exploring implications for black hole spin limits.

Contribution

It provides a new, straightforward formula for predicting the final black hole spin from initial parameters, enhancing understanding of merger dynamics and spin evolution.

Findings

The formula accurately reproduces numerical simulation results.

It suggests black holes cannot reach extremal spins through mergers.

The approach helps identify configurations leading to interesting angular momentum dynamics.

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.