Emergent Turbulence in Nonlinear Gravity

TL;DR

This paper uncovers nonlinear interactions in full General Relativity that can cause inverse energy cascades and turbulence, offering new insights into gravitational phenomena from cosmology to black hole mergers.

Contribution

It demonstrates the emergence of specific nonlinear interactions and turbulence transitions in full General Relativity, extending previous perturbative findings to the nonlinear regime.

Findings

Identification of four-mode and three-mode nonlinear interactions.

Evidence of inverse energy cascades and resonant instabilities.

Observation of a laminar-turbulent transition for large angular structures.

Abstract

Gravity in nonlinear and dynamical regimes underpins spectacular astrophysical phenomena and observable consequences, from the early universe to black hole collisions. In these extreme environments, inverse energy cascades - mediated by nonlinear interactions - may help explain the near scale-invariance of cosmic structure and the simplicity of gravitational waves from binary black hole mergers. Yet the presence, characteristics, and generality of such interactions in full General Relativity remain largely unexplored. Here we show that two types of nonlinear interactions - a four-mode and a three-mode interaction - emerge in the fully nonlinear regime, and can indeed channel inverse energy cascades by inducing resonant and anti-damping instabilities. This establishes what was previously only hinted at in highly specialized perturbative contexts. We further demonstrate a ``laminar'' to ``turbulent'' transition for the largest-possible angular structure in General Relativity, whereas finer structures remain persistently turbulent. Our results reveal the impact and generality of these nonlinear interactions (instabilities), which can be key to understanding observations ranging from cosmological to kilometer scales. We anticipate that our work will shed new light on nonlinear gravitational phenomena and their consequences, such as constructing gravitational wave templates and testing General Relativity in the most extreme regime. Moreover, our work is a starting point for addressing nonlinear gravitational interactions using ideas and methods inspired by fluid dynamics.