Coalescence of Two Spinning Black Holes: An Effective One-Body Approach

TL;DR

This paper extends the effective one-body approach to spinning black hole binaries, improving the modeling of their dynamics and gravitational wave signals, especially near the last stable orbits, with implications for gravitational wave detection.

Contribution

It generalizes the effective one-body method to include black hole spins, enhancing the analytical modeling of binary dynamics and gravitational waveforms for spinning black hole systems.

Findings

Improved post-Newtonian convergence for spinning black holes.

Identification of last stable spherical orbits relevant for gravitational wave detection.

Prediction that the final black hole spin remains sub-extremal after coalescence.

Abstract

We generalize to the case of spinning black holes a recently introduced ``effective one-body'' approach to the general relativistic dynamics of binary systems. The combination of the effective one-body approach, and of a Pad\'e definition of some crucial effective radial functions, is shown to define a dynamics with much improved post-Newtonian convergence properties, even for black hole separations of the order of $6 GM / c^2$. We discuss the approximate existence of a two-parameter family of ``spherical orbits'' (with constant radius), and, of a corresponding one-parameter family of ``last stable spherical orbits'' (LSSO). These orbits are of special interest for forthcoming LIGO/VIRGO/GEO gravitational wave observations. It is argued that for most (but not all) of the parameter space of two spinning holes the effective one-body approach gives a reliable analytical tool for describing the dynamics of the last orbits before coalescence. This tool predicts, in a quantitative way, how certain spin orientations increase the binding energy of the LSSO. This leads to a detection bias, in LIGO/VIRGO/GEO observations, favouring spinning black hole systems, and makes it urgent to complete the conservative effective one-body dynamics given here by adding (resummed) radiation reaction effects, and by constructing gravitational waveform templates that include spin effects. Finally, our approach predicts that the spin of the final hole formed by the coalescence of two arbitrarily spinning holes never approaches extremality.