A Covariant Mechanism for Kerr Singularity Regularization via U(1) Noether Currents

Within the framework of Effective Field Theory (EFT), classical spacetime singularities represent an ultraviolet (UV) breakdown of the macroscopic gravitational action rather than a physical inevitability. In stationary axisymmetric backgrounds, classically described by the Kerr geometry, this UV breakdown manifests as a pathological ring singularity allowing for chronological violations. Attempts to regularize these regions typically rely on ad-hoc phenomenological imperfect fluids lacking a microphysical origin. Here, we propose a covariant, field-theoretic UV regularization mechanism derived from a non-perturbative scalar-tensor action. Operating within a ghost-free modulated framework, we model the macroscopic matter sector as the infrared (IR) projection of an internal U(1) topological multiplet. Our analysis indicates that off-diagonal spacetime angular momentum can be covariantly sourced by the fundamental Noether phase current (∇_μ θ), analogous to quantized vortices in relativistic superfluids. Through asymptotic limits combined with a self-consistent 2D numerical Banach–Sobolev relaxation of the coupled Einstein-scalar equations over a stationary background, we show how extreme spatial curvature gradients naturally drive the scalar amplitude to a finite UV saturation limit. This localized kinetic suppression drastically damps rotational frame-dragging at the core, supporting an internal mass profile with cubic scaling (M ∝ Σ³). Explicit 2D tensor evaluations verify that within this stationary background, the classical Kerr ring singularity is replaced by a non-singular, toroidal Kerr–de Sitter core possessing globally bounded curvature invariants (R, R_μν R^μν, and the Kretschmann scalar K). By maintaining a non-negative azimuthal metric that effectively mitigates the formation of Closed Timelike Curves (CTCs) across the stationary manifold, this approach offers a causally well-behaved relativistic groundwork, establishing a fully regular stationary background for future non-linear dynamical investigations.