  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.
