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

Alessandro Nagar, Enno Harms, Sebastiano Bernuzzi, Anıl Zenginoğlu

December, 2014

### 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 $ν≪1$. Extending previous studies to nearly extremal negative spins, thus complementing current numerical relativity knowledge about the recoil, we find that the well-known decrease of the antikick is overturned and, instead of approaching zero, the antikick increases again to reach $Δv/(cν^2)=3.37×10^{−3}$ for dimensionless spin $\hat{a}=−0.9999$. The corresponding final kick velocity is $v_{end}/(cν^2)=0.076$. We interpret the antikick result analytically by means of the quality factor $Q$ of the linear momentum flux, that is used to quantify the amount of nonadiabaticity of the emission process. We show that, besides capturing qualitatively the global properties over the whole spin range, $Q$ actually predicts the return of the antikick for $\hat{a}\to−1$. Since $Q$ is computed only from the, gauge-invariant, flux of linear momentum, the herein presented verification of its reliability advocates its systematic use also in numerical relativity calculations. In addition, we also connect, in a new way, the properties of the flux to the noncircular character of the plunge dynamics, highlighting the central role of subdominant waveform multipoles in shaping the characteristic interference pattern exhibited by the linear momentum flux as $\hat{a}\to−1$.

Publication

*Physical Review D*