Remnant group of local Lorentz transformations in f(T) theories

Abstract

It is shown that the extended teleparallel gravitational theories, known as f(T) theories, inherit some on shell local Lorentz invariance associated with the tetrad field defining the spacetime structure. We discuss some enlightening examples, such as Minkowski spacetime and cosmological (Friedmann-Robertson-Walker and Bianchi type I) manifolds. In the first case, we show that the absence of gravity reveals itself as an incapability in the selection of a preferred parallelization at a local level, due to the fact that the infinitesimal local Lorentz subgroup acts as a symmetry group of the frame characterizing Minkowski spacetime. Finite transformations are also discussed in these examples and, contrary to the common lore on the subject, we conclude that the set of tetrads responsible for the parallelization of these manifolds is quite vast and that the remnant group of local Lorentz transformations includes one and two dimensional Abelian subgroups of the Lorentz group.

arXiv comment10 pages. Minor changes. To appear in PRD

References in corpus (23)

• f(R) Theories Of Gravity
• Dark torsion as the cosmic speed-up
• Modified teleparallel gravity: inflation without inflaton
• Einstein's Other Gravity and the Acceleration of the Universe
• f(T) Gravity and local Lorentz invariance
• On Born-Infeld Gravity in Weitzenbock spacetime
• Teleparallel equivalent of Gauss-Bonnet gravity and its modifications
• Generalizations of teleparallel gravity and local Lorentz symmetry
• Good and bad tetrads in f(T) gravity
• Large-scale Structure in f(T) Gravity
• Non trivial frames for f(T) theories of gravity and beyond
• Degrees of freedom of $f(T)$ gravity
• Spherically symmetric static spacetimes in vacuum f(T) gravity
• Cosmological applications of $F(T,T_G)$ gravity
• Cosmological Perturbation in f(T) Gravity Revisited
• Problems with Propagation and Time Evolution in f(T) Gravity
• Covariance properties and regularization of conserved currents in tetrad gravity
• Normal frames for non-Riemannian connections
• Cosmological frames for theories with absolute parallelism
• Matter Density Perturbations in Modified Teleparallel Theories
• Acausality and Nonunique Evolution in Generalized Teleparallel Gravity
• Born-Infeld Determinantal gravity and the taming of the conical singularity in 3-dimensional spacetime
• Compact extra dimensions in cosmologies with f(T) structure

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• The effective field theory approach of teleparallel gravity, $f(T)$ gravity and beyond
• Modified teleparallel theories of gravity -- Gauss-Bonnet and trace extensions
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