Nonlinear Effects In Black Hole Ringdown From Scattering Experiments I: spin and initial data dependence of quadratic mode coupling

TL;DR

This study explores quadratic mode coupling in black hole ringdowns through simulations, revealing its dependence on spin and initial data, and highlighting potential for testing nonlinear GR effects with gravitational wave detectors.

Contribution

It demonstrates the insensitivity of quadratic mode coupling coefficients to initial data variations and provides evidence of bifurcation related to black hole spin.

Findings

Good agreement between numerical relativity and perturbation theory within 10%.

Coupling coefficients are insensitive to diverse initial data.

Evidence of bifurcation in coupling coefficients with increasing spin.

Abstract

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 $\ell=|m|=2$ quadrupolar modes, we find good agreement (within $\sim10\%$) 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.