A new gravitational wave generation algorithm for particle perturbations of the Kerr spacetime

Abstract

We present a new approach to solve the 2+1 Teukolsky equation for gravitational perturbations of a Kerr black hole. Our approach relies on a new horizon penetrating, hyperboloidal foliation of Kerr spacetime and spatial compactification. In particular, we present a framework for waveform generation from point-particle perturbations. Extensive tests of a time domain implementation in the Teukode code are presented. The code can efficiently deliver waveforms at future null infinity. The accuracy and convergence of the waveforms' phase and amplitude is demonstrated. As a first application of the method, we compute the gravitational waveforms from inspiraling and coalescing black-hole binaries in the large-mass-ratio limit. The smaller mass black hole is modeled as a point particle whose dynamics is driven by an effective-one-body-resummed analytical radiation reaction force. We compare the analytical, mechanical angular momentum loss (computed using two different prescriptions) to the gravitational wave angular momentum flux. We find that higher-order post-Newtonian corrections are needed to improve the consistency for rapidly spinning binaries. We characterize the multipolar waveform as a function of the black-hole spin. Close to merger, the subdominant multipolar amplitudes (notably the m = 0 ones) are enhanced for retrograde orbits with respect to prograde ones. We argue that this effect mirrors nonnegligible deviations from the circularity of the dynamics during the late-plunge and merger phase. For the first time, we compute the gravitational wave energy flux flowing into the black hole during the inspiral using a time-domain formalism proposed by Poisson. Finally, a self-consistent, iterative method to compute the gravitational wave fluxes at leading-order in the mass of the particle is developed. The method can be used alternatively to the analytical radiation reaction in cases where the analytical information is poor or not sufficient. Specifically, we apply it to compute dynamics and waveforms for a rapidly rotating black hole with dimensionless spin parameter _(â = + 0.9). For this case, the simulation with the consistent flux differs from the one with the analytical flux by ~ 35 gravitational wave cycles over a total of about 250 cycles. In this simulation the horizon absorption accounts for about +5 gravitational wave cycles.

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