Conjecture on the suitability of gauge-invariant metric variables

Establish whether the gauge-invariant transverse–traceless metric components (h^{TT}_{xx}, h^{TT}_{yy}, h^{TT}_{xy}, h^{TT}_{zz}) constitute more natural physical-space variables than the canonical variables for analysing gravitational wave turbulence.

Background

The authors compare statistics of canonical variables with those of gauge-invariant metric components. They observe near-Gaussian behaviour with intermittent events for canonical variables, whereas the structure functions of gauge-invariant components exhibit largely monofractal behaviour typical of wave turbulence.

Based on these observations, they propose a conjecture that gauge-invariant variables are better suited for physical-space analysis of gravitational wave turbulence.