Nonlinear Dynamics in General Relativity

TL;DR

This paper explores new nonlinear phenomena in general relativity, including harmonic generation and spectral effects, revealing complex behaviors in gravitational systems and implications for interpreting gravitational wave signals.

Contribution

It uncovers novel nonlinear effects in Einstein's equations, such as higher harmonic generation and spectral broadening, expanding understanding of gravitational dynamics.

Findings

Higher harmonic generation in Einstein Klein-Gordon system

Spectral broadening and focusing effects observed

Weak sensitivity of wave scattering to frequency at large wavelengths

Abstract

Black holes and gravitational waves are consequences of the nonlinear character of the Einstein equations. Yet, the remarkable properties of General Relativity point to the existence of other effects. Here we uncover new nonlinear facets of gravity. We establish higher harmonic generation, spectral broadening and focusing in the Einstein Klein-Gordon system. In vacuum, we show that scattering of monochromatic waves at quadratic order is weakly sensitive to frequency, at large wavelengths. These aspects can both explain the seemingly smooth behavior of mergers, but also caution us against too simplistic an interpretation of waveforms.