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Quasinormal modes and their excitation beyond general relativity. II. Isospectrality loss in gravitational waveforms

Hector O. Silva1,2, Giovanni Tambalo3, Kostas Glampedakis4,5, and Kent Yagi6

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Phys. Rev. D 113, 084012 – Published 7 April, 2026

DOI: https://doi.org/10.1103/lgfg-lvjn

Abstract

We continue our series of papers where we study the quasinormal modes, and their excitation, of black holes in the simplest beyond general relativity model in which first-principle calculations are tractable: a nonrotating black hole in an effective-field-theory extension of general relativity with cubic-in-curvature terms. In this theory, the equivalence between the quasinormal mode spectra associated with metric perturbations of polar and axial parities (“isospectrality”) of the Schwarzschild black hole in general relativity no longer holds. How does this loss of isospectrality translate into the time-domain ringdown of gravitational waves? Given such a ringdown, can we identify the two “fundamental quasinormal modes” associated to the two metric-perturbation parities? We study these questions through a large suite of time-domain numerical simulations, by a prescription on how to relate the gauge-invariant master functions that describe metric perturbations of each parity with the gravitational polarizations. Under the assumptions made in our calculations, we find that it is in general difficult to identify either of the two fundamental modes from the time series, although finding evidence for a non-general-relativistic mode is possible sometimes. We discuss our results in light of our assumptions and speculate about what may occur when they are relaxed.

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Quasinormal modes and their excitation beyond general relativity

Hector O. Silva, Giovanni Tambalo, Kostas Glampedakis, Kent Yagi, and Jan Steinhoff
Phys. Rev. D 110, 024042 (2024)

Article Text

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Phys. Rev. D 113, 084012– Published 7 April, 2026
  • Received 25 January 2026
  • Accepted 12 March 2026
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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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