The antikick strikes back: recoil velocities for nearly-extremal binary black hole mergers in the test-mass limit

TL;DR

This paper investigates the recoil velocities of nearly-extremal binary black hole mergers in the test-mass limit, revealing that the antikick increases for high negative spins, contrary to previous expectations, and introduces a new analytical interpretation using a quality factor.

Contribution

The study extends previous perturbative analyses to nearly-extremal negative spins, showing the antikick increases instead of decreases, and introduces a new analytical tool based on the flux quality factor.

Findings

Antikick increases for high negative spins, reaching a maximum at $ ext{a}=-0.9999$

The final kick velocity is significantly larger than previously predicted for these spins

A new analytical interpretation using the flux quality factor explains the nonadiabatic emission of linear momentum.

Abstract

Gravitational waves emitted from a generic binary black-hole merger carry away linear momentum anisotropically, resulting in a gravitational recoil, or "kick", of the center of mass. For certain merger configurations the time evolution of the magnitude of the kick velocity has a local maximum followed by a sudden drop. Perturbative studies of this "antikick" in a limited range of black hole spins have found that the antikick decreases for retrograde orbits as a function of negative spin. We analyze this problem using a recently developed code to evolve gravitational perturbations from a point-particle in Kerr spacetime driven by an effective-one-body resummed radiation reaction force at linear order in the mass ratio $\nu\ll 1$. Extending previous studies to nearly-extremal negative spins, we find that the well-known decrease of the antikick is overturned and, instead of approaching zero, the antikick increases again to reach $\Delta v/(c\nu^{2})=3.37\times10^{-3}$ for dimensionless spin $\hat{a}=-0.9999$. The corresponding final kick velocity is $v_{end}/(c\nu^{2})=0.076$. This result is connected to the nonadiabatic character of the emission of linear momentum during the plunge. We interpret it analytically by means of the quality factor of the flux to capture quantitatively the main properties of the kick velocity. The use of such quality factor of the flux does not require trajectories nor horizon curvature distributions and should therefore be useful both in perturbation theory and numerical relativity.