arXiv subjects

Elisa Varani

Publications and source records attributed to Elisa Varani.

5 recordsLinked to original sources

arXiv2026

Spin Induced Geometry: Emergence of Metric and Torsional Sectors from Spinor Source

We present a geometric framework in which both metric and torsional degrees of freedom emerge dynamically from spinor currents, without being postulated as fundamental properties of the affine connection. The fundamental dynamical variable is a rank-three field carrying local Lorentz indices, governed by a massive Klein--Gordon equation sourced by fermionic spin currents. Its projection onto spacetime indices yields a rank-two tensor with no definite symmetry; the symmetric and antisymmetric sectors define, respectively, an effective spin-induced metric and the torsional degrees of freedom. Both sectors are massive and Yukawa-suppressed, ensuring decoupling from long-range gravitational dynamics. Unlike Einstein--Cartan theory, torsion here is propagating rather than algebraically constrained. A key consequence is that spinless test particles follow geodesics of the effective metric and are therefore indirectly sensitive to spin currents through the emergent geometric structure~ -- ~a mechanism absent in both standard General Relativity and Einstein--Cartan theory. The spinorial structure of the source is analyzed across three regimes: general Dirac, Weyl, and Majorana fermions, each giving rise to a distinct geometric phase. In the Majorana limit, the geometry becomes purely axial-torsional, admitting topologically non-trivial configurations such as vortices and Skyrmion-like structures, which emerge dynamically from the spinorial source.

gr-qc↗

arXiv2025

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

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.

gr-qc↗

arXiv2025

Torsional Effects in the Coupling between Gravity and Spinors -- Yukawa Gravity

We study spinors in the framework of general relativity, starting from the Dirac field Lagrangian in the approximation of weak gravity. We focus on how fermions couple to gravity through the spin connection, and we analyze these couplings by analogy with the Ginzburg-Landau model and the Yukawa interaction known from the Higgs mechanism. By solving the field equations, we explore how these couplings affect the spacetime metric. In particular, torsion generated by fermionic spin currents naturally emerges and leads to the breaking of Lorentz symmetry. As a consequence, gravity acquires a mass and fermions gain additional mass contributions through their interaction with this gravitational field. These effects are localized and diminish quickly with distance. Our model offers an alternative explanation to phenomena usually attributed to dark matter and dark energy. We link these cosmological effects to chirality-flip processes of Majorana neutrinos interacting with a massive graviton. Right-handed Majorana neutrinos, which are sterile under Standard Model interactions, generate repulsive gravitational curvature and act as a source of dark energy, while left-handed neutrinos contribute to attractive gravitational effects akin to dark matter. The spin-gravity coupling modifies the curvature of spacetime, influencing galaxy rotation, the accelerated expansion of the universe, and the bending of light. In short, the intrinsic spin of fermions, when coupled to gravity via torsion, changes gravity from a long-range, massless force to a short-range, massive one. This new framework provides fresh insights into fundamental physics and cosmology, potentially explaining dark matter and dark energy phenomena through spin-related gravitational effects.

gr-qc↗

arXiv2022

Fermionic current in general relativity

In general relativity the affine connection is required to be symmetric so torsion is zero while according to the Einsten- Cartan's theory torsion is connected to the spin tensor as expressed by the Cartan's equations. We consider the theory of spinors in general relativity in the light of the results of Einstein Cartan's theory.In general relativity the affine connection is required to be symmetric so torsion is zero while according to the Einsten- Cartan's theory torsion is connected to the spin tensor as expressed by the Cartan's equations. We consider the theory of spinors in general relativity in the light of the results of Einstein Cartan's theory. This work begins with the study of the spin connection coefficients, the calculation of the canonical momenta detects a spinor rotational current; fermionic rotational current is associated with torsion as explained by Cartan's equations, we find this torsion contribution even if the affine connection is symmetric. In the final considerations, we analyze the interaction terms (as written in the full action for Dirac spinors) and we compare them with the results of linearized gravity. We deduce that Gravitomagnetism is well described in the linearized theory while the term of spin connection giving rise to fermionic current is canceled out, so we mean these terms are describing different interactions.

gr-qc↗

arXiv2011

Gravitomagnetism and spinor quantum mechanics

We give a systematic treatment of a spin 1/2 particle in a combined electromagnetic field and a weak gravitational field that is produced by a slowly moving matter source. This paper continues previous work on a spin zero particle, but it is largely self-contained and may serve as an introduction to spinors in a Riemann space. The analysis is based on the Dirac equation expressed in generally covariant form and coupled minimally to the electromagnetic field. The restriction to a slowly moving matter source, such as the earth, allows us to describe the gravitational field by a gravitoelectric (Newtonian) potential and a gravitomagnetic (frame-dragging) vector potential, the existence of which has recently been experimentally verified. Our main interest is the coupling of the orbital and spin angular momenta of the particle to the gravitomagnetic field. Specifically we calculate the gravitational gyromagnetic ratio as gsubg=1 ; this is to be compared with the electromagnetic gyromagnetic ratio of gsube=2 for a Dirac electron.

gr-qc↗