Reflections on the covariance of modified teleparallel theories of gravity

Abstract

We review the current status of the Lorentz covariance in teleparallel and modified teleparallel theories of gravity, and discuss the controversial features of the different approaches. We also revisit the issue of the remnant Lorentz gauge symmetries in $f(T)$ gravity.

12 pages, no figures; contribution to the proceedings of the workshop "Teleparallel Universes in Salamanca"

References in corpus (8)

• Dark torsion as the cosmic speed-up
• Modified teleparallel gravity: inflation without inflaton
• Cosmological perturbations in f(T) gravity
• Generalizations of teleparallel gravity and local Lorentz symmetry
• Conformal transformation in $f(T)$ theories
• Remnant group of local Lorentz transformations in f(T) theories
• Hamiltonian formulation of teleparallel gravity
• The regular black hole in four dimensional Born-Infeld gravity

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• Bianchi identities in f(T) gravity: paving the way to confrontation with astrophysics
• Issues of Lorentz-invariance in f(T) gravity and calculations for spherically symmetric solutions
• Dynamical complexity of the Teleparallel gravity cosmology
• General cosmological perturbations in teleparallel gravity
• Post-Newtonian limit of generalized scalar-torsion theories of gravity
• Lorentz gauge-invariant variables in torsion-based theories of gravity
• Boson stars in $f(T)$ extended theory of gravity
• Bounce Models within Teleparallel modified gravity
• Disformal transformations in modified teleparallel gravity
• Unexplored regions in teleparallel $f(T)$ gravity: Sign-changing dark energy density
• BTZ gems inside regular Born-Infeld black holes
• The geometrical meaning of the Weitzenböck connection
• Irregular universe in the Nieh-Yan modified teleparallel gravity
• A geometric view on local Lorentz transformations in teleparallel gravity
• Matching tetrads in f(T) gravity
• Gravitational Waves in New General Relativity
• Tangent space symmetries in general relativity and teleparallelism
• Role of the remnant symmetries in gravitational theories based on absolute parallelism: a 2D standpoint
• Chronology protection in $f(T)$ gravity: the case of Gott's pair of moving cosmic strings
• Local symmetries in $f(T)$-like models: lessons from 2D