Einstein-Cartan theory of gravity revisited

TL;DR

This paper revisits Einstein-Cartan gravity, proposing a new volume element compatible with torsion, deriving modified equations, and exploring novel features such as torsion propagation and gauge interactions.

Contribution

It introduces a new volume element for Einstein-Cartan theory, derives the associated dynamical equations, and discusses novel predictions like torsion propagation and gauge invariance.

Findings

Torsion propagates in Einstein-Cartan theory.

Gauge fields can interact with torsion without breaking gauge invariance.

A new Einstein-Hilbert action offers a physical interpretation for dilaton gravity.

Abstract

The role of space-time torsion in general relativity is reviewed in accordance with some recent results on the subject. It is shown that, according to the connection compatibility condition, the usual Riemannian volume element is not appropriate in the presence of torsion. A new volume element is proposed and used in the Lagrangian formulation for Einstein-Cartan theory of gravity. The dynamical equations for the space-time geometry and for matter fields are obtained, and some of their new predictions and features are discussed. In particular, one has that torsion propagates and that gauge fields can interact with torsion without the breaking of gauge invariance. It is shown also that the new Einstein-Hilbert action for Einstein-Cartan theory may provide a physical interpretation for dilaton gravity in terms of the non-riemannian structure of space-time.