Possible discovery of a nonlinear tail and second-order quasinormal modes in black hole ringdown

TL;DR

This paper explores the nonlinear aspects of black hole ringdown, revealing the existence of second-order quasinormal modes and a novel power-law tail that could impact gravitational wave analysis.

Contribution

It demonstrates the excitation of second-order QNMs at new frequencies and uncovers a slow-decaying second-order tail, advancing understanding of nonlinear black hole dynamics.

Findings

Second-order QNMs are excited at different frequencies.

A new second-order power-law tail dominates late-time evolution.

Nonlinear effects are significant for binary black hole mergers.

Abstract

We investigate the nonlinear evolution of black hole ringdown in the framework of higher-order metric perturbation theory. By solving the initial-value problem of a simplified nonlinear field model analytically as well as numerically, we find that (i) second-order quasinormal modes (QNMs) are indeed excited at frequencies different from those of first-order QNMs, as predicted recently. We also find serendipitously that (ii) late-time evolution is dominated by a new type of power-law tail. This ``second-order power-law tail'' decays more slowly than any late-time tails known in the first-order (i.e., linear) perturbation theory, and is generated at the wavefront of the first-order perturbation by an essentially nonlinear mechanism. These nonlinear components should be particularly significant for binary black hole coalescences, and could open a new precision science in gravitational wave studies.