Nonlinear Dynamics in General Relativity

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.