A Covariant Mechanism for Kerr Singularity Regularization via U(1) Noether Currents
Year: 2026
Type: preprint
Abstract: 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.
Author: Chakchaev, Adam
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7203682742
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