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.

10 pages. Minor changes. To appear in PRD

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• Reflections on the covariance of modified teleparallel theories of gravity
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• On the role of constraints and degrees of freedom in the Hamiltonian formalism
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• BTZ gems inside regular Born-Infeld black holes
• A geometric view on local Lorentz transformations in teleparallel gravity
• New proper tetrad for teleparallel gravities in non-flat spacetime
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