Nonlinear effects in the black hole ringdown: Absorption-induced mode excitation

Gravitational-wave observations of black hole ringdowns are commonly used to characterize binary merger remnants and to test general relativity. These analyses assume linear black hole perturbation theory, in particular that the ringdown can be described in terms of quasinormal modes even for times approaching the merger. Here we investigate a nonlinear effect during the ringdown, namely how a mode excited at early times can excite additional modes as it is absorbed by the black hole. This is a third-order secular effect: the change in the black hole mass causes a shift in the mode spectrum, so that the original mode is projected onto the new ones. Using nonlinear simulations, we study the ringdown of a spherically symmetric scalar field around an asymptotically anti-de Sitter black hole, and we find that this absorption-induced mode excitation is the dominant nonlinear effect. We show that this effect takes place well within the nonadiabatic regime, so we can analytically estimate it using a sudden mass-change approximation. Adapting our estimation technique to asymptotically flat Schwarzschild black holes, we expect absorptioninduced mode excitation to play a role in the analysis and interpretation of current and future gravitational wave observations.

Automated summary

This paper investigates a nonlinear effect during the ringdown process, namely the absorption-induced mode excitation, which is found to be the dominant nonlinear effect. The study shows that this effect occurs within the nonadiabatic regime and proposes an estimation technique.