Rotating Emergent Metric (PSE‑Kerr): Structural Extension of the PSE Framework

The parameter  appearing in the PSE Kerr metric is the same emergent rigidity parameter defined in the radial domain. It is not introduced as a new constant: it is the continuous projection of the discrete rigidity associated with the stable configurations γ ⊂ Γ, obtained through the monotonic sub‑map Φrig ⊂ Φgeom . Rotation modifies the emergent structure Ce_rot, but does not introduce a new rigidity: γ remains the original geometric rigidity controlling metric saturation also in the rotating case.

The PSE rotating metric is the original emergent geometry associated with spin in the Structural Principle of Entanglement (PSE). It does not arise from modifications of the Kerr metric nor from any regularization procedure: it is generated directly by the pregeometric ontological chain

S → Ds(f) → Cf → Ds(e) → Ce → Φgeom → {d, g{μν}},

where the rotating emergent correlation Ce^rot possesses intrinsic rigidity and intrinsic saturation. These properties prevent divergences, ensure metric continuity, and keep the internal structure regular even in high‑spin regimes.

The geometric projection Φgeom constructs the rotating physical metric {d, g{μν}}^rot = Φgeom(Ds(e), Ce^rot), yielding a continuous, non‑divergent geometry that remains compatible with the classical angular structure. The only element distinguishing the PSE rotating metric from the classical Kerr metric is the emergent rotating deviation ε_rot(r, θ): it is not a free parameter, not a phenomenological term, but the mathematical signature of the emergent correlation and its saturation.

This construction leads to a rotating geometry that remains regular at all radii and exhibits a controlled deviation from Kerr in the deep interior. The resulting metric provides a coherent, non‑singular description of high‑spin regimes within the PSE framework.

The Kerr metric is used solely as a weak‑field coherence limit and as a phenomenological reference. The PSE rotating metric is therefore an original emergent geometry, not a correction to the classical metric.

Author: Andrea Toricelli
independent researcher
Email: a.toricelli@hotmail.it