Semi-Teleparallel Theories of Gravitation

TL;DR

This paper introduces a class of gravitation theories based on a geometry with preferred frames, combining Riemann-Cartan and teleparallel features, and explores their field equations and coupling to spinor fields.

Contribution

It presents a novel class of gravitation theories with preferred frames using a partial parallelization of space-time, unifying Riemann-Cartan and teleparallel geometries.

Findings

Derived field equations for the proposed geometry.

Constructed action functionals using a variational approach.

Discussed coupling of the theory to spinor fields.

Abstract

A class of theories of gravitation that naturally incorporates preferred frames of reference is presented. The underlying space-time geometry consists of a partial parallelization of space-time and has properties of Riemann-Cartan as well as teleparallel geometry. Within this geometry, the kinematic quantities of preferred frames are associated with torsion fields. Using a variational method, it is shown in which way action functionals for this geometry can be constructed. For a special action the field equations are derived and the coupling to spinor fields is discussed.