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.

arXiv comment12 pages, no figures; contribution to the proceedings of the workshop "Teleparallel Universes in Salamanca"

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Cited by in corpus (32)

• Teleparallel Theories of Gravity: Illuminating a Fully Invariant Approach
• Modified teleparallel theories of gravity in symmetric spacetimes
• Stable and self-consistent compact star models in teleparallel gravity
• Black Holes in $f(T,B)$ Gravity: Exact and Perturbed Solutions
• Modified gravity: a unified approach
• Conformally symmetric traversable wormholes in modified teleparallel gravity
• Minkowski space in $f(T)$ gravity
• 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
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• Pseudoinvariance and the extra degree of freedom in f(T) gravity
• Dynamical complexity of the Teleparallel gravity cosmology
• General cosmological perturbations in teleparallel gravity
• Post-Newtonian limit of generalized scalar-torsion theories of gravity
• Post-Newtonian limit of scalar-torsion theories of gravity as analogue to scalar-curvature theories
• Lorentz gauge-invariant variables in torsion-based theories of gravity
• Difficulties of Teleparallel Theories of Gravity with Local Lorentz Symmetry
• 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
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• Chronology protection in $f(T)$ gravity: the case of Gott's pair of moving cosmic strings
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• Local symmetries in $f(T)$-like models: lessons from 2D