The squared magnetic Weyl tensor behaves as an approximately conserved gravitational enstrophy, giving a Fjørtoft-type constraint that pushes nonlinear gravitational-wave energy toward lower frequencies in near-extremal Kerr and AdS.
The fractional enstrophy loss through the horizon is F Z H+ δZ/τ nl ∼ ω2 Rκ+ ω2 R ·ϵ 2ωR = κ+ ϵ2ωR → κ+ mΩH (ϵ∼O(1))
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Gravitational Enstrophy: Local Geometric Origin and Inverse-Cascade Constraints
The squared magnetic Weyl tensor behaves as an approximately conserved gravitational enstrophy, giving a Fjørtoft-type constraint that pushes nonlinear gravitational-wave energy toward lower frequencies in near-extremal Kerr and AdS.