Selected Topics in Teleparallel Gravity

TL;DR

This paper explores teleparallel gravity as a gauge theory, highlighting its unique features such as independence from the equivalence principle and its Maxwell-like structure, with applications to particle motion and quantum effects.

Contribution

It presents a gauge-theoretic formulation of teleparallel gravity, emphasizing its differences from general relativity and discussing applications to quantum gravitational phenomena.

Findings

Teleparallel gravity does not rely on the equivalence principle.

It admits a global formulation similar to Maxwell's theory.

Applications include particle motion and quantum gravitational effects.

Abstract

Teleparallel gravity can be seen as a gauge theory for the translation group. As such, its fundamental field is neither the tetrad nor the metric, but a gauge potential assuming values in the Lie algebra of the translation group. This gauge character makes of teleparallel gravity, despite its equivalence to general relativity, a rather peculiar theory. A first important point is that it does not rely on the universality of free fall, and consequently does not require the equivalence principle to describe the gravitational interaction. Another peculiarity is its similarity with Maxwell's theory, which allows an Abelian nonintegrable phase factor approach, and consequently a global formulation for gravitation. Application of these concepts to the motion of spinless particles, as well as to the COW and gravitational Aharonov-Bohm effects are presented and discussed.