Direct Evidence of a Dual Cascade in Gravitational Wave Turbulence

Galtier, Sebastien; Nazarenko, Sergey V.

doi:10.48550/arxiv.2108.09158

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2022

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“…The relevance of these questions for modern astrophysics and cosmology cannot be overstated [3][4][5][6][7][8][9][10][11], and this work represents a preliminary attempt to gain semiquantitative insights into the above matters.…”

Section: Introductionmentioning

confidence: 99%

First Post-Minkowskian approach to turbulent gravity

Bini¹,

Kauffman²,

Succi³

et al. 2022

Preprint

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We compute the metric fluctuations induced by a turbulent energy-matter tensor within the first order Post-Minkowskian approximation. It is found that the turbulent energy cascade can in principle interfere with the process of black hole formation, leading to a potentially strong coupling between these two highly nonlinear phenomena. It is further found that a power-law turbulent energy spectrum E(k) ∼ k −n generates metric fluctuations scaling like x n−2 , where x is a four-dimensional distance from an arbitrary origin in spacetime. This highlights the onset of metric singularities whenever n < 2, meaning that 2d fluid turbulence (n = 3) yields smooth metric fluctuations, scaling like x, while 3d turbulence (n = 5/3) yields a weakly singular metric x −1/3 and purely random fluctuations, n = 1, generate a stronger 1/x singularity. Finally, the effect of metric fluctuations on the geodesic motion of test particles is also discussed as a potential technique to extract information on the spectral characteristics of fluctuating spacetime.

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