Binary–Black-Hole Merger: Symmetry and the Spin Expansion

We regard binary–black-hole (BBH) merger as a map from a simple initial state (two Kerr black holes, with dimensionless spins a and b) to a simple final state (a Kerr black hole with mass m, dimensionless spin s, and kick velocity k). By expanding this map around a=b=0 and applying symmetry constraints, we obtain a simple formalism that is remarkably successful at explaining existing BBH simulations. It also makes detailed predictions and suggests a more efficient way of mapping the parameter space of binary black-hole merger. Since we rely on symmetry rather than dynamics, our expansion complements previous analytical techniques.