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

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) the evolution is dominated by a new type of power-law tail at late times. 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 wave front 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.