Lorentz gauge-invariant variables in torsion-based theories of gravity

Abstract

General relativity dynamics can be derived from different actions -- which depart from the Einstein-Hilbert action in boundary terms -- and for different choices of the dynamical variables. Among them, the teleparallel equivalent of general relativity is a torsion-based theory for the tetrad field. More general torsion-based theories have been built in the last years, intending to supersede general relativity. There are two current ways to formulate such theories; one includes a spin-connection and the other does not. We discuss the notion of Lorentz gauge invariance in such theories, and give a simple but important proof that both formulations are physically equivalent.

7 pages, matches the published version

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• The geometrical meaning of the Weitzenböck connection
• Tetrad Fields, Reference Frames, and the Gravitational Energy-Momentum in the Teleparallel Equivalent of General Relativity
• The Gauss-Bonnet topological scalar in the Geometric Trinity of Gravity
• On the degrees of freedom count on singular phase space submanifolds
• Static spherically symmetric solutions in New General Relativity
• Gravitational Waves in New General Relativity
• Teleparallel bigravity
• Degrees of Freedom in modified Teleparallel Gravity
• Teleparallel dark energy in a nonflat universe
• Dark matter effects in modified teleparallel gravity
• Chronology protection in $f(T)$ gravity: the case of Gott's pair of moving cosmic strings
• Foliation-generating observers under Lorentz transformations
• Local symmetries in $f(T)$-like models: lessons from 2D
• Translation gauge field theory of gravity in Minkowski spacetime