Emergence of Lorentz Symmetry Violation in Rotating Black Holes from the Universal Ψ Lagrangian

This paper demonstrates that the Lorentz symmetry violation parameter ℓ introducedin Kerr–like and Bumblebee gravity models emerges naturally from the intrinsiccoherence structure of the Universal Ψ Lagrangian. The deviation of local metric symmetryin rotating black holes arises as a small imbalance in the informational constraint(Ψ†Ψ−1)2, without any external field or spontaneous symmetry–breaking mechanism.By linearizing the Ψ field around the Kerr background, we obtain a correction term tothe metric coefficients identical in form to the ℓ–dependent modification of Bumblebeegravity. The derived lensing observables θ∞, s, and rmag match the values measured bythe EHT for Sgr A* and M87* within |ℓΨ|≲10−6, confirming the astrophysical validityof the Ψ framework.