Hybrid method for understanding black-hole mergers: Inspiralling case

TL;DR

This paper develops a hybrid analytical method combining post-Newtonian and black-hole-perturbation theories to model black-hole binary inspirals, producing waveforms that closely match numerical simulations and explaining phenomena like spin precession and recoil kicks.

Contribution

It introduces a self-consistent hybrid approach with radiation-reaction effects for inspiral waveforms and analyzes spin dynamics and recoil in black-hole mergers.

Findings

Generated inspiral-merger-ringdown waveforms match numerical results in phase.

Observed phase locking of quadrupole modes during ringdown.

Reproduced recoil kicks consistent with numerical simulations.

Abstract

We adapt a method of matching post-Newtonian and black-hole-perturbation theories on a timelike surface (which proved useful for understanding head-on black-hole-binary collisions) to treat equal-mass, inspiralling black-hole binaries. We first introduce a radiation-reaction potential into this method, and we show that it leads to a self-consistent set of equations that describe the simultaneous evolution of the waveform and of the timelike matching surface. This allows us to produce a full inspiral-merger-ringdown waveform of the l=2, m=2,-2 modes of the gravitational waveform of an equal-mass black-hole-binary inspiral. These modes match those of numerical-relativity simulations well in phase, though less well in amplitude for the inspiral. As a second application of this method, we study a merger of black holes with spins antialigned in the orbital plane (the "superkick" configuration). During the ringdown of the superkick, the phases of the mass- and current-quadrupole radiation become locked together, because they evolve at the same quasinormal mode frequencies. We argue that this locking begins during merger, and we show that if the spins of the black holes evolve via geodetic precession in the perturbed black-hole spacetime of our model, then the spins precess at the orbital frequency during merger. In turn, this gives rise to the correct behavior of the radiation, and produces a kick similar to that observed in numerical simulations.