Mode coupling in the nonlinear response of black holes

TL;DR

This paper investigates the nonlinear gravitational wave response of non-spinning black holes to ingoing waves using numerical simulations, revealing significant nonlinear effects absent in linear models.

Contribution

It extends previous linear analyses to the fully nonlinear regime, uncovering new features of gravitational wave emission from black holes.

Findings

Large phase shifts in gravitational waves

Enhanced nonlinear generation of radiation

Generation of polarization states not present in linear theory

Abstract

We study the properties of the outgoing gravitational wave produced when a non-spinning black hole is excited by an ingoing gravitational wave. Simulations using a numerical code for solving Einstein's equations allow the study to be extended from the linearized approximation, where the system is treated as a perturbed Schwarzschild black hole, to the fully nonlinear regime. Several nonlinear features are found which bear importance to the data analysis of gravitational waves. When compared to the results obtained in the linearized approximation, we observe large phase shifts, a stronger than linear generation of gravitational wave output and considerable generation of radiation in polarization states which are not found in the linearized approximation. In terms of a spherical harmonic decomposition, the nonlinear properties of the harmonic amplitudes have simple scaling properties which offer an economical way to catalog the details of the waves produced in such black hole processes.