Metric-affine approach to teleparallel gravity

TL;DR

This paper presents a systematic metric-affine framework for teleparallel gravity, deriving symmetries, conservation laws, and field equations, and discusses its advantages and limitations, especially regarding spinning matter sources.

Contribution

It introduces a comprehensive metric-affine approach to teleparallel gravity, unifying physical and geometric perspectives, and analyzes its features and issues.

Findings

The teleparallel GR-equivalent model has distinctive attractive features.

The model faces a consistency problem with spinning matter sources.

A systematic derivation of symmetries and conservation laws is provided.

Abstract

The teleparallel gravity theory, treated physically as a gauge theory of translations, naturally represents a particular case of the most general gauge-theoretic model based on the general affine group of spacetime. On the other hand, geometrically, the Weitzenboeck spacetime of distant parallelism is a particular case of the general metric-affine spacetime manifold. These physical and geometrical facts offer a new approach to the teleparallelism. We present a systematic treatment of the teleparallel gravity within the framework of the metric-affine theory. The symmetries, conservation laws and the field equations are consistently derived, and the physical consequences are discussed in detail. We demonstrate that the so-called teleparallel GR-equivalent model has a number of attractive features which distinguishes it among the general teleparallel theories, although it has a consistency problem when dealing with spinning matter sources.