The Einstein-Cartan-Elko system

TL;DR

This paper explores how Elko spinors influence Einstein-Cartan gravity, revealing a richer torsion structure and offering solutions to coupling Maxwell fields, advancing understanding of spinor-torsion interactions.

Contribution

It introduces the coupling of Elko spinors to Einstein-Cartan theory, showing a more complex torsion structure and addressing Maxwell field coupling issues.

Findings

Elko spinors produce a richer torsion structure than Dirac spinors.

Elko spinors help partially solve Maxwell field coupling problems.

The spin angular momentum tensor of Elko spinors is derived and analyzed.

Abstract

The present paper analyses the Einstein-Cartan theory of gravitation with Elko spinors as sources of curvature and torsion. After minimally coupling the Elko spinors to torsion, the spin angular momentum tensor is derived and its structure is discussed. It shows a much richer structure than the Dirac analogue and hence it is demonstrated that spin one half particles do not necessarily yield only an axial vector torsion component. Moreover, it is argued that the presence of Elko spinors partially solves the problem of minimally coupling Maxwell fields to Einstein-Cartan theory.