Binary black hole merger: symmetry and the spin expansion

TL;DR

This paper introduces a symmetry-based expansion formalism to model binary black hole mergers, effectively predicting outcomes and improving parameter space mapping without relying on detailed dynamics.

Contribution

It develops a symmetry-constrained spin expansion approach that simplifies understanding and predicting binary black hole merger outcomes.

Findings

Successfully explains existing BBH simulation results

Predicts detailed merger outcomes based on initial spins

Proposes a more efficient parameter space mapping method

Abstract

We regard binary black hole (BBH) merger as a map from a simple initial state (two Kerr black holes, with dimensionless spins {\bf a} and {\bf b}) to a simple final state (a Kerr black hole with mass m, dimensionless spin {\bf s}, and kick velocity {\bf k}). By expanding this map around {\bf a} = {\bf 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.