Peaking into the abyss: Characterizing the merger of equatorial-eccentric-geodesic plunges in rotating black holes

Abstract

We study the gravitational waveforms generated by critical, equatorial plunging geodesics of the Kerr metric that start from an unstable-circular-orbit, which describe the test-mass limit of spin-aligned eccentric black-hole mergers. The waveforms are generated employing a time-domain Teukolsky code. We span different values of the Kerr spin $-0.99\le a\le 0.99$ and of the critical eccentricity $e_c$, for bound ($0\le e_c<1$) and unbound plunges ($e_c\ge 1$). We find that, contrary to expectations, the waveform modes $h_{\ell m}$ do not always manifest a peak for high eccentricities or spins. In case of the dominant $h_{22}$ mode, we determine the precise region of the parameter space in which its peak exists. In this region, we provide a characterization of the merger quantities of the $h_{22}$ mode and of the higher-order modes, providing the merger structure of the equatorial eccentric plunges of the Kerr spacetime in the test-mass limit.

29 pages, 16 figures

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Cited by in corpus (3)

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• Particles with precessing spin in Kerr spacetime: analytic solutions for eccentric orbits and homoclinic motion near the equatorial plane