Flag-Dipole Spinor Fields in ESK Gravities

TL;DR

This paper explores flag-dipole spinor fields within Einstein-Sciama-Kibble gravities, revealing solutions that challenge traditional spinor classifications and have implications for cosmology and the structure of matter.

Contribution

It demonstrates that in certain gravitational theories, solutions to the Dirac equation can be flag-dipole spinors, highlighting the importance of algebraic properties in spinor dynamics.

Findings

Flag-dipole spinor solutions exist in specific gravitational backgrounds.

Such solutions are relevant for understanding spinor behavior in cosmology.

They challenge the notion that spinor fields are solely determined by their dynamics.

Abstract

We consider the Riemann-Cartan geometry as a basis for the Einstein-Sciama-Kibble theory coupled to spinor fields: we focus on $f(R)$ and conformal gravities, regarding the flag-dipole spinor fields, type-(4) spinor fields under the Lounesto classification. We study such theories in specific cases given for instance by cosmological scenarios: we find that in such background the Dirac equation admits solutions that are not Dirac spinor fields, but in fact the aforementioned flag-dipoles ones. These solutions are important from a theoretical perspective, as they evince that spinor fields are not necessarily determined by their dynamics, but also a discussion on their structural (algebraic) properties must be carried off. Furthermore, the phenomenological point of view is shown to be also relevant, since for isotropic Universes they circumvent the question whether spinor fields do undergo the Cosmological Principle.