Teleparallel gravity (TEGR) as a gauge theory: Translation or Cartan connection?

Abstract

In this paper we question the status of TEGR, the Teleparallel Equivalent of General Relativity,as a gauge theory of translations. We observe that TEGR (in its usual translation-gauge view) does not seem to realize the generally admitted requirements for a gauge theory for some symmetry group $G$: namely it does not present a mathematical structure underlying the theory which relates to a principal $G$-bundle and the choice of a connection on it (the gauge field). We point out that, while it is usually presented as absent, the gauging of the Lorentz symmetry is actually present in the theory, and that the choice of an Erhesmann connection to describe the gauge field makes the translations difficult to implement (mainly because there is in general no principal translation-bundle). We finally propose to use the Cartan Geometry and the Cartan connection as an alternative approach, naturally arising from the solution of the issues just mentioned, to obtain a more mathematically sound framework for TEGR.

12pp, 8 figs

References in corpus (2)

• Coincident General Relativity
• Geometrical Foundations of Cartan Gauge Gravity

Cited by in corpus (22)

• Teleparallel Gravity: From Theory to Cosmology
• $f(Q,T)$ gravity
• Weyl type $f(Q,T)$ gravity, and its cosmological implications
• Modified teleparallel theories of gravity in symmetric spacetimes
• Generalizing the coupling between geometry and matter: $f(R,L_m,T)$ gravity
• Gauge Structure of Teleparallel Gravity
• Model parameters in the context of late time cosmic acceleration in $f(Q,T)$ gravity
• Non-minimal geometry-matter couplings in Weyl-Cartan space-times: $f(R,T,Q,T_m)$ gravity
• Noether charge and black hole entropy in teleparallel gravity
• The General Linear Cartan Khronon
• $f(Q,L_m)$ gravity, and its cosmological implications
• Teleparallel theory as a gauge theory of translations: comments and issues
• Constrained transit cosmological models in $f(R,L_m,T)$-gravity
• From Barthel Randers Kropina Geometries to the Accelerating Universe: A Brief Review of Recent Advances in Finslerian Cosmology
• Teleparallel gravity as a gauge theory: coupling to matter with Cartan connection
• Cartan approach to Teleparallel Equivalent to General Relativity: a review
• Tangent space symmetries in general relativity and teleparallelism
• The meaning of torsion in teleparallel theories
• Focusing conditions for extended teleparallel gravity theories
• Conservation laws in gauge gravity theory
• Towards a unified theory of the fundamental physical interactions based on the underlying geometric structure of the tangent bundle
• Translation gauge field theory of gravity in Minkowski spacetime