We investigate quadratic quasinormal mode coupling in black hole spacetime through numerical simulations of single perturbed black holes using both numerical relativity and second-order black hole perturbation theory. Focusing on the dominant ℓ=∣m∣=2 quadrupolar modes, we find good agreement (within ∼10%) between these approaches, with discrepancies attributed to truncation error and uncertainties from mode fitting. Our results align with earlier studies extracting the coupling coefficients from select binary black hole merger simulations, showing consistency for the same remnant spins. Notably, the coupling coefficient is insensitive to a diverse range of initial data, including configurations that led to a significant (up to 5%) increase in the remnant black hole mass. These findings present opportunities for testing the nonlinear dynamics of general relativity with ground-based gravitational wave observatories. Lastly, we provide evidence of a bifurcation in coupling coefficients between counter-rotating and co-rotating quasinormal modes as black hole spin increases.
@article{arxiv.2401.00805,
title = {Nonlinear Effects In Black Hole Ringdown From Scattering Experiments I: spin and initial data dependence of quadratic mode coupling},
author = {Hengrui Zhu and Justin L. Ripley and Frans Pretorius and Sizheng Ma and Keefe Mitman and Robert Owen and Michael Boyle and Yitian Chen and Nils Deppe and Lawrence E. Kidder and Jordan Moxon and Kyle C. Nelli and Harald P. Pfeiffer and Mark A. Scheel and William Throwe and Nils L. Vu},
journal= {arXiv preprint arXiv:2401.00805},
year = {2024}
}