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Quasinormal ringing of Kerr black holes. III. Excitation coefficients for equatorial inspirals from the innermost stable circular orbit

Matteo Della Rocca1,2,3,*, Laura Pezzella4,5,6,†, Emanuele Berti6,‡, Leonardo Gualtieri2,7,§, and Andrea Maselli4,5,∥

  • *Contact author: matteo.dellarocca@uniroma1.it
  • †Contact author: laura.pezzella@gssi.it
  • ‡Contact author: berti@jhu.edu
  • §Contact author: leonardo.gualtieri@unipi.it
  • ∥Contact author: andrea.maselli@gssi.it
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Phys. Rev. D 114, 044036 – Published 11 August, 2026

DOI: https://doi.org/10.1103/ydp5-ktpn

Abstract

The remnant of a black hole binary merger settles into a stationary configuration by “ringing down” through the emission of gravitational waves that consist of a superposition of damped exponentials with discrete complex frequencies—the remnant black hole’s quasinormal modes. While the frequencies themselves depend solely on the mass and spin of the remnant, the mode amplitudes depend on the merger dynamics. We investigate quasinormal mode excitation by a point particle plunging from the innermost stable circular orbit of a Kerr black hole. Our formalism is general, but we focus on computing the quasinormal mode excitation coefficients in the frequency domain for equatorial orbits, and we analyze their dependence on the remnant black hole spin. We find that higher overtones and subdominant multipoles of the radiation become increasingly significant for rapidly rotating black holes. This suggests that the prospects for detecting overtones and higher-order modes are considerably enhanced for highly spinning merger remnants.

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Phys. Rev. D 114, 044036– Published 11 August, 2026
  • Received 14 January 2026
  • Accepted 8 June 2026
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