## Abstract

We study binary black hole mergers in the extreme mass-ratio limit. We determine the energy, angular momentum, and linear momentum of the post-merger, remnant black hole. Unlike previous works, we perform our analysis directly in the test-particle limit by solving the Regge-Wheeler-Zerilli wave equation with a source that moves along a geodesic. We rely on the fact that toward the merger, small mass-ratio binary systems follow a quasiuniversal geodesic trajectory. This formalism captures the final premerger stages of small mass-ratio binaries and thus provides a straightforward universal description in a region inaccessible to numerical relativity simulations. We present a general waveform template that may be used in the search for gravitational wave bursts from small and intermediate mass-ratio binary systems. Finally, this formalism gives a formal proof that the recoil velocity is quadratic in the symmetric mass ratio ν. Specifically, the velocity is given by V/c≈0.0467ν2. This result is about 4% larger than previously estimated. Most of this difference stems from the inclusion of higher multipoles in our calculation.

Original language | American English |
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Article number | 104040 |

Journal | Physical Review D |

Volume | 106 |

Issue number | 10 |

DOIs | |

State | Published - 15 Nov 2022 |

### Bibliographical note

Funding Information:The authors would like to thank Scott Hughes, Amos Ori, and Tsvi Piran for useful comments. This research was partially supported by an ISF grant.

Publisher Copyright:

© 2022 American Physical Society.