2026/08/04 by Luis Lehner
Physics and Astronomy · #astro-ph.HE #gr-qc #hep-th
Two-dimensional fluids conserve energy and enstrophy, driving inverse energy cascades via Fjørtoft's argument. We show General Relativity admits an analogous structure: for linear radiative perturbations of Petrov type D backgrounds (Kerr, Kerr--AdS), the gravitational-wave energy W = ∑k Wk and magnetic Weyl enstrophy Z = ∫ Bab Bab √γ d3x ≈ ∑k ωk2 Wk are approximately conserved in the zero-angular momentum frame, where vorticity coupling vanishes identically and curl exchange cancels mode-by-mode. This yields a gravitational Fjørtoft constraintt implyging nonlinear energy transfer proceeds preferentially toward lower frequencies. The constraint is dynamically active in near-extremal Kerr (τdamp ≫ τnl) and confined geometries (AdS), but suppressed in generic ringdown. In AdS, Z maps holographically to the boundary fluid enstrophy.