Cubic Quasinormal Modes in the Black-Hole Ringdown
Abstract
We formulate and numerically solve the nonlinear Teukolsky equations through third order, obtaining a first-principles calculation of cubic quasinormal-mode amplitudes for Kerr black holes. Our approach combines lower-order metric reconstruction in split light-cone gauges with a hyperboloidal, compactified formulation solved on complex radial contours. Spin-dependent complex coupling coefficients fix the cubic amplitudes from products of their linear parent amplitudes. We apply these predictions to a nonprecessing numerical-relativity waveform, including cubic products of the (2,2) fundamental mode, its first overtone, and their conjugates. The predicted cubic terms improve agreement over selected early-ringdown fitting windows and shift inferred linear-overtone amplitudes without adding fitting parameters. 3M after the peak of |h22|, the summed cubic contribution reaches approximately 38% of the total h22 signal; M is the initial total mass. These results identify an appreciable cubic response in early ringdown.
Related
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- Black-Hole Ringdown from Photon-Sphere Modes in an Elastic Analogue
- Quasinormal modes of a quantum inspired black hole in four dimensions with cosmological constant
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- Quasinormal modes of Reissner-Nordström black hole from bound state spectrum
BibTeX
@misc{khera2026cubic,
title = {{Cubic Quasinormal Modes in the Black-Hole Ringdown}},
author = {Neev Khera and Huan Yang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.20547},
eprint = {2610.20547},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.20547},
}
RIS
TY - UNPB
TI - Cubic Quasinormal Modes in the Black-Hole Ringdown
AU - Neev Khera
AU - Huan Yang
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.20547
UR - https://arxiv.org/abs/2610.20547
AB - We formulate and numerically solve the nonlinear Teukolsky equations through third order, obtaining a first-principles calculation of cubic quasinormal-mode amplitudes for Kerr black holes. Our approach combines lower-order metric reconstruction in split light-cone gauges with a hyperboloidal, compactified formulation solved on complex radial contours. Spin-dependent complex coupling coefficients fix the cubic amplitudes from products of their linear parent amplitudes. We apply these predictions to a nonprecessing numerical-relativity waveform, including cubic products of the (2,2) fundamental mode, its first overtone, and their conjugates. The predicted cubic terms improve agreement over selected early-ringdown fitting windows and shift inferred linear-overtone amplitudes without adding fitting parameters. 3M after the peak of |h_22|, the summed cubic contribution reaches approximately 38% of the total h_22 signal; M is the initial total mass. These results identify an appreciable cubic response in early ringdown.
ER -