Duerr, Patrick M. and Read, James
(2025)
Clarifying the foundations of Teleparallel Gravity: translational gauge freedom vs. local Lorentz invariance.
[Preprint]
Abstract
Teleparallel Gravity (TPG) is an alternative, but empirically equivalent, spacetime theory to General Relativity. Rather than as a manifestation of spacetime curvature, TPG conceptualises gravitational degrees of freedom as a manifestation of spacetime torsion. In its modern formulation (as presented e.g. in the book-length study by Aldrovandi and Pereira (2013)), TPG also and expressly purports to be both a gauge theory of translations (G), as well as locally Lorentz-invariant (L). However, the reasoning which these authors invoke in order to implement (L) and (G) is often involved; indeed its mathematical coherence seems on occasion to be questionable. As such, clarification of the reasoning upon which TPG proponents rely in constructing the theory is sorely needed. The present paper will address this need. More broadly, we aim at achieving three interrelated tasks: (i) to shed light on TPG's aspirations of maintaining (G) and (L) at the same time, (ii) to illuminate TPG's conceptual and interpretative structure, and (iii) to offer a succinct methodological assessment of TPG as a theory per se.
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