Year: 2026
Type: preprint
Abstract: Two-dimensional incompressible fluids conserve energy and enstrophy in the inviscid limit. Fjørtoft's argument uses this pair to constrain nonlinear energy transfer. We examine the corresponding question in General Relativity using the magnetic Weyl functional $\mathcal Z=\int B_{ab}B^{ab}\sqrtγ\,d^3x$. Its transverse radiativ e part carries an additional frequency-squared weight relative to gravitational-wave energy: $δ\mathcal Z_k\simeqω_k^2W_k$ in the radiation zone, with $W=8πG E_{\rm GW}$. We derive its balance law from the Bianchi identities, obtaining the algebraic cancellations, bulk sources and boundary fluxes. Conservation of positive e nergy and curvature norm through nonlinear transfer gives a Fjørtoft constraint when their weights are ordered. Resonant weak-wave interactions generally change the c urvature norm; $2\leftrightarrow2$ dynamics instead conserves energy and wave action. We examine the competition between transfer and linear losses in Kerr and AdS backg rounds, where long-lived or confined modes provide time for nonlinear evolution. In the hydrodynamic regime of AdS$_4$, a fluid-weighted magnetic Weyl functional inherit s fluid enstrophy conservation in the inviscid limit. We compute its proportionality coefficient to boundary enstrophy in closed form at leading gradient order, giving a bulk diagnostic for holographic turbulence.
Source: arXiv (Cornell University)
Author: Lehner, Luis
Institution: Perimeter Institute
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7172494963