Wave turbulence theory for gravitational waves in general relativity: The Space-Time Kolmogorov spectrum

TL;DR

This paper applies wave turbulence theory to gravitational waves in general relativity, proposing a Kolmogorov spectrum for space-time fluctuations and discussing implications for gravitational astronomy and tests of Einstein's theory.

Contribution

It introduces a kinetic wave turbulence framework for gravitational waves, predicting a Kolmogorov-Zakharov spectrum for space-time fluctuations in general relativity.

Findings

Evidence of wave turbulence spectra in gravitational wave signals

Prediction of a non-equilibrium Kolmogorov-Zakharov spectrum

Implications for gravitational wave observations and tests of gravity

Abstract

The recent observation of gravitational waves, stimulates the question of the longtime evolution of the space-time fluctuations. Gravitational waves interact themselves through the nonlinear character of Einstein's equations of general relativity. This nonlinear wave interaction allows the spectral energy transfer from mode to mode. According to the wave turbulence theory, the weakly nonlinear interaction of gravitational waves leads to the existence of an irreversible kinetic regime that dominates the longtime evolution. The resulting kinetic equation suggests the existence of an equilibrium wave spectrum and the existence of a non-equilibrium Kolmogorov-Zakharov spectrum for spatio-temporal fluctuations. Evidence of these solutions extracted in the fluctuating signal of the recent observations will be discussed in the paper. Probably, the present results would be pertinent in the new age of development of gravitational astronomy, as well as, in new tests of General Relativity.