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

Elisa Varani

TL;DR

This work shows that stationary torsional configurations can arise in linearized gravity when driven by coherent chiral Majorana neutrino currents. By adopting a Ricci-flow–inspired relaxation of the metric perturbation, the authors identify curvature-negligible fixed points sustained by chiral sources, and classify these configurations using topological invariants: a holonomy $\Phi_T = \oint A^g_\mu dx^\mu = 2\pi n$ associated with $\pi_1(S^1)$ and a skyrmion charge $Q_S$ from $\pi_3(S^3)$. Two concrete stationary geometries are presented: toroidal skyrmion-like domains stabilized by $Q_S$ and Möbius-like non-orientable bridges arising from the chiral-flip sector, both with a finite-range, Yukawa-type gravitational response governed by a coherence length $\mu^{-1}$ via $G(\mathbf{x},\mathbf{x}')$. The results reveal a purely torsional mechanism by which coherent chiral currents can influence effective gravity in neutrino-rich environments, potentially impacting astrophysical and cosmological settings in ways explored further in the companion study Varani2025.

Abstract

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 metric 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 stabilized by topological invariants associated with the fundamental groups pi1(S1) and pi3(S3). Toroidal skyrmionic domains emerge when one chirality dominates, whereas a chiral-flip interference sector enables Moebius-type non-orientable bridges between opposite-chirality regions. In the static limit, a Green-function formulation provides a finite-range Yukawa-type 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.

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

TL;DR

This work shows that stationary torsional configurations can arise in linearized gravity when driven by coherent chiral Majorana neutrino currents. By adopting a Ricci-flow–inspired relaxation of the metric perturbation, the authors identify curvature-negligible fixed points sustained by chiral sources, and classify these configurations using topological invariants: a holonomy associated with and a skyrmion charge from . Two concrete stationary geometries are presented: toroidal skyrmion-like domains stabilized by and Möbius-like non-orientable bridges arising from the chiral-flip sector, both with a finite-range, Yukawa-type gravitational response governed by a coherence length via . The results reveal a purely torsional mechanism by which coherent chiral currents can influence effective gravity in neutrino-rich environments, potentially impacting astrophysical and cosmological settings in ways explored further in the companion study Varani2025.

Abstract

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 metric 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 stabilized by topological invariants associated with the fundamental groups pi1(S1) and pi3(S3). Toroidal skyrmionic domains emerge when one chirality dominates, whereas a chiral-flip interference sector enables Moebius-type non-orientable bridges between opposite-chirality regions. In the static limit, a Green-function formulation provides a finite-range Yukawa-type 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.

Paper Structure

This paper contains 12 sections, 10 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Chiral currents and weak--field setting
  3. Ricci flow evolution
  4. Left/right and chiral-flip contributions
  5. Topological characterization
  6. Holonomy and torsional vortices
  7. Skyrmionic torsion and toroidal domains
  8. Examples of stationary torsional domains
  9. Toroidal stationary domain (skyrmion-like)
  10. Chiral-flip stitching: Möbius-like bridge
  11. Static limit and Green-function formulation
  12. Conclusion

Figures (2)

  • Figure 1: Schematic Möbius-like torsional bridge generated by chiral-flip stitching between domains of opposite chirality. Local curvature remains negligible while the global holonomy is non-trivial.
  • Figure 2: Schematic toroidal torsional domain supported by circulating chiral currents. The torsional geometry is globally stable due to a non-zero skyrmion charge.