Direct Evidence of a Dual Cascade in Gravitational Wave Turbulence

We present the first direct numerical simulation of gravitational wave turbulence. General relativity equations are solved numerically in a periodic box with a diagonal metric tensor depending on two space coordinates only, g(ij) g(ii) (x, y, t)delta(ij), and with an additional small-scale dissipative term. We limit ourselves to weak gravitational waves and to a freely decaying turbulence. We find that an initial metric excitation at intermediate wave number leads to a dual cascade of energy and wave action. When the direct energy cascade reaches the dissipative scales, a transition is observed in the temporal evolution of energy from a plateau to a power-law decay, while the inverse cascade front continues to propagate toward low wave numbers. The wave number and frequency-wave-number spectra are found to be compatible with the theory of weak wave turbulence and the characteristic timescale of the dual cascade is that expected for four-wave resonant interactions. The simulation reveals that an initially weak gravitational wave turbulence tends to become strong as the inverse cascade of wave action progresses with a selective amplification of the fluctuations g(11) and g(22).

Automated summary

The study conducts the first direct numerical simulation of gravitational wave turbulence under the constraints of weak gravitational waves and freely decaying turbulence. It reveals a dual cascade of energy and wave action, as well as selective amplification of wave fluctuations during the inverse cascade process.