Nonlinear ringdown at the black hole horizon

TL;DR

This paper demonstrates the presence of nonlinear quadratic modes in the horizon data of newly formed black holes after head-on collisions, extending the understanding of black hole ringdown beyond linear perturbation theory.

Contribution

It identifies and characterizes quadratic nonlinear modes in black hole horizons, showing their relationship with linear modes in head-on collision simulations.

Findings

Quadratic modes are present in the horizon shear data.

Quadratic mode amplitudes relate quadratically to linear mode amplitudes.

Nonlinear effects are significant in black hole ringdown analysis.

Abstract

The gravitational waves emitted by a perturbed black hole ringing down are well described by damped sinusoids, whose frequencies are those of quasinormal modes. Typically, first-order black hole perturbation theory is used to calculate these frequencies. Recently, it was shown that second-order effects are necessary in binary black hole merger simulations to model the gravitational-wave signal observed by a distant observer. Here, we show that the horizon of a newly formed black hole after the head-on collision of two black holes also shows evidence of non-linear modes. Specifically, we identify one quadratic mode for the $l=2$ shear data, and two quadratic ones for the $l=4,6$ data in simulations with varying mass ratio and boost parameter. The quadratic mode amplitudes display a quadratic relationship with the amplitudes of the linear modes that generate them.