Torsion waves in metric-affine field theory

TL;DR

This paper explores torsion wave solutions in metric-affine field theory, identifying specific spacetime configurations that could model neutrinos and their properties.

Contribution

It introduces a family of torsion wave solutions in metric-affine theory and proposes a model for neutrinos based on these solutions.

Findings

Identified torsion wave solutions in Minkowski space.

Discovered a subfamily with zero Ricci curvature related to Einstein equations.

Suggested a natural particle model with neutrino-like particles.

Abstract

The approach of metric-affine field theory is to define spacetime as a real oriented 4-manifold equipped with a metric and an affine connection. The 10 independent components of the metric tensor and the 64 connection coefficients are the unknowns of the theory. We write the Yang-Mills action for the affine connection and vary it both with respect to the metric and the connection. We find a family of spacetimes which are stationary points. These spacetimes are waves of torsion in Minkowski space. We then find a special subfamily of spacetimes with zero Ricci curvature; the latter condition is the Einstein equation describing the absence of sources of gravitation. A detailed examination of this special subfamily suggests the possibility of using it to model the neutrino. Our model naturally contains only two distinct types of particles which may be identified with left-handed neutrinos and right-handed antineutrinos.