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We investigate the nonlinear evolution of black hole ringdown in theframework of higher-order metric perturbation theory. By solving theinitial-value problem of a simplified nonlinear field model analytically aswell as numerically, we find that (i) second-order quasinormal modes (QNMs) areindeed excited at frequencies different from those of first-order QNMs, aspredicted recently. We also find serendipitously that (ii) late-time evolutionis dominated by a new type of power-law tail. This ``second-order power-lawtail'' 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 thefirst-order perturbation by an essentially nonlinear mechanism. These nonlinearcomponents should be particularly significant for binary black holecoalescences, and could open a new precision science in gravitational wavestudies.

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