Non-linear harmonic generation in finite amplitude black hole oscillations

TL;DR

This study investigates how black holes generate harmonics through non-linear gravitational perturbations using numerical relativity, revealing that black holes predominantly respond at the initial perturbation mode and tend to smooth out angular distortions.

Contribution

It provides a detailed numerical analysis of non-linear harmonic generation in black hole oscillations, highlighting the dominance of response at the initial mode and the balance of scattering processes.

Findings

Black holes respond mainly at the initial perturbation harmonic.

Down-scattering effectively smooths angular distortions.

Black holes tend to avoid fission despite strong perturbations.

Abstract

The non-linear generation of harmonics in gravitational perturbations of black holes is explored using numerical relativity based on an in-going light-cone framework. Localised, finite, perturbations of an isolated black hole are parametrised by amplitude and angular harmonic form. The response of the black hole spacetime is monitored and its harmonic content analysed to identify the strength of the non-linear generation of harmonics as a function of the initial data amplitude. It is found that overwhelmingly the black hole responds at the harmonic mode perturbed, even for spacetimes with 10% of the black hole mass radiated. The relative efficiencies of down and up-scattering in harmonic space are computed for a range of couplings. Down-scattering, leading to smoothing out of angular structure is found to be equally or more efficient than the up-scatterings that would lead to increased rippling. The details of this non-linear balance may form the quantitative mechanism by which black holes avoid fission even for arbitrary strong distortions.