Angle-Quantized Spacetime Circulation Around Rotating SMBHs: An Effective Field-Theoretic Framework for Angular Sector Structure and Emergent Mass Hierarchies

Abstract

Abstract This preprint presents a phenomenological effective field-theoretic framework for investigating angular structure around rotating supermassive black holes. A real scalar order parameter with a symmetry-breaking quartic potential, non-minimal curvature coupling, and Yukawa-type interaction is considered on a stationary axisymmetric Kerr background. The model employs a truncated Legendre expansion containing the monopole, quadrupole, and hexadecapole contributions to explore polar, intermediate, and equatorial angular regimes. Conditions for a sector-dependent ordering of the scalar amplitude and effective mass scale are examined. Local inverse-length estimates are distinguished from the global radial decay behavior of the field modes. A phenomenological time-flow parameter and a tentative correspondence between angular regimes and fermion-generation labels are introduced as hypotheses rather than established consequences of the underlying action. Possible observational implications include anisotropic maser emission, angular spectral shifts, jet–disk energy contrasts, and intermediate-angle high-energy emission. The framework is intended as an exploratory theoretical model. Its proposed astrophysical signatures require further dynamical calculations and observational tests. Version note: Version 1.0 is a mathematically revised preprint based on the original manuscript dated 27 April 2026. It has not undergone peer review.