Topologically Stabilized Torsion in Weak-Field Gravity: A Ricci–Flow Framework

Abstract

Elisa Varani*

We investigate stationary torsional configurations supported by chiral Majorana neutrino currents in linearized gravity. A Ricci–flow–inspired geometric relaxation (with no physical time interpretation) is introduced to drive the tetrad perturbation toward fixed points sustained by chiral sources while keeping curvature invariants negligible. We show that divergence-free chiral currents can support globally non-trivial torsional holonomy, classified by π_1 (S^1), and that three-dimensional torsional domains admit an independent winding classification associated with π_3 (S^3). Toroidal skyrmionic domains emerge when one chirality dominates, whereas a chiral-flip interference sector supports Möbius-type bridges between opposite-chirality regions, characterized by a Z_2 spinorial holonomy associated with π_1 (SO(3)). In the static limit, a Green-function formulation provides a finite-range Yukawatype response governed by the neutrino coherence length. These results identify a purely torsional mechanism independent of local curvature through which coherent chiral currents may influence effective gravitational behavior in neutrino-rich environments.

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