The Nonlinear Tails in Black Hole Ringdown: the Scattering Perspective

Black holes regain their static configuration by emitting ringdown gravitational waves, whose amplitude decays in time following a power law at fixed spatial positions. We show that the nonlinear decay power law may be obtained by simple scattering calculations using the in-in formalism and argue that the nonperturbative law should be $t^{-2\mathrm{\ell }-1}$, where $\mathrm{\ell }$ is the multipole of the propagating spherical gravitational wave.