Due to the nature of gravity, non-linear effects are left imprinted in the quasi-normal modes generated in the ringdown phase of the merger of two black holes. We offer an analytical treatment of the quasi-normal modes at second-order in black hole perturbation theory which takes advantage from the fact that the non-linear sources are peaked around the light ring. As a byproduct, we describe why the amplitude of the second-order mode relative to the square of the first-order amplitude depends only weakly on the initial condition of the problem.
@article{arxiv.2308.15886,
title = {Non-linear Black Hole Ringdowns: an Analytical Approach},
author = {Davide Perrone and Thomas Barreira and Alex Kehagias and Antonio Riotto},
journal= {arXiv preprint arXiv:2308.15886},
year = {2024}
}