The Nonlinear Tails in Black Hole Ringdown: the Scattering Perspective

TL;DR

This paper investigates the nonlinear decay tails in black hole ringdown gravitational waves, proposing a scattering perspective that predicts a specific power-law decay based on multipole moments.

Contribution

It introduces a scattering-based method using the in-in formalism to derive the nonlinear decay law in black hole ringdown signals.

Findings

Nonlinear decay follows a power law of t^{-2ℓ-1}.

The scattering perspective effectively predicts decay behavior.

The nonperturbative law is supported by the analysis.

Abstract

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 $t^{-2\ell-1}$, where $\ell$ is the multipole of the propagating spherical gravitational wave.