Direct Evidence of a Dual Cascade in Gravitational Wave Turbulence
Abstract
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_{i j}≡g_{i i}(x ,y ,t )δ_{i j}, and with an additional smallscale 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 powerlaw decay, while the inverse cascade front continues to propagate toward low wave numbers. The wave number and frequencywavenumber 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 fourwave 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}.
 Publication:

Physical Review Letters
 Pub Date:
 September 2021
 DOI:
 10.1103/PhysRevLett.127.131101
 arXiv:
 arXiv:2108.09158
 Bibcode:
 2021PhRvL.127m1101G
 Keywords:

 General Relativity and Quantum Cosmology
 EPrint:
 6 figures, 6 pages