First Post-Minkowskian approach to turbulent gravity

We compute the metric fluctuations induced by a turbulent energy-matter tensor within the first orderpost-Minkowskian approximation. It is found that the turbulent energy cascade can in principle interferewith the process of black hole formation, leading to a potentially strong coupling between these two highlynonlinear phenomena. It is further found that a power-law turbulent energy spectrum EðkÞ ~ k-n generatesmetric fluctuations scaling as xn-2, where x is the four-dimensional spacelike distance from an arbitraryorigin in Minkowski spacetime, highlighting the onset of metric singularities whenever n < 2. Finally, theeffect of metric fluctuations on the geodesic motion of test particles is also discussed as a potentialtechnique to extract information on the spectral characteristics of fluctuating spacetime.