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Nonlinear effects in the black hole ringdown: Absorption-induced mode excitation

Laura Sberna1,*, Pablo Bosch2, William E. East3, Stephen R. Green1, and Luis Lehner3

  • 1Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Am Mühlenberg 1, 14476 Potsdam, Germany
  • 2GRAPPA and Institute of High-Energy Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, Netherlands
  • 3Perimeter Institute, 31 Caroline Street North, N2L 2Y5 Ontario, Canada

  • *laura.sberna@aei.mpg.de
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Phys. Rev. D 105, 064046 – Published 28 March, 2022

DOI: https://doi.org/10.1103/PhysRevD.105.064046

Abstract

Gravitational-wave observations of black hole ringdowns are commonly used to characterize binary merger remnants and to test general relativity. These analyses assume linear black hole perturbation theory, in particular that the ringdown can be described in terms of quasinormal modes even for times approaching the merger. Here we investigate a nonlinear effect during the ringdown, namely how a mode excited at early times can excite additional modes as it is absorbed by the black hole. This is a third-order secular effect: the change in the black hole mass causes a shift in the mode spectrum, so that the original mode is projected onto the new ones. Using nonlinear simulations, we study the ringdown of a spherically symmetric scalar field around an asymptotically anti–de Sitter black hole, and we find that this “absorption-induced mode excitation” is the dominant nonlinear effect. We show that this effect takes place well within the nonadiabatic regime, so we can analytically estimate it using a sudden mass-change approximation. Adapting our estimation technique to asymptotically flat Schwarzschild black holes, we expect absorption-induced mode excitation to play a role in the analysis and interpretation of current and future gravitational wave observations.

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Phys. Rev. D 105, 064046– Published 28 March, 2022
  • Received 12 January 2022
  • Accepted 1 March 2022
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Open access publication funded by the Max Planck Society.

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