Good and bad tetrads in f(T) gravity

Abstract

We investigate the importance of choosing good tetrads for the study of the field equations of $f(T)$ gravity. It is well known that this theory is not invariant under local Lorentz transformations, and therefore the choice of tetrad plays a crucial role in such models. Different tetrads will lead to different field equations which in turn have different solutions. We suggest to speak of a good tetrad if it imposes no restrictions on the form of $f(T)$. Employing local rotations, we construct good tetrads in the context of homogeneity and isotropy, and spherical symmetry, where we show how to find Schwarzschild-de Sitter solutions in vacuum. Our principal approach should be applicable to other symmetries as well.

25 pages

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Cited by in corpus (29)

• Teleparallel equivalent of Gauss-Bonnet gravity and its modifications
• Cosmological Solutions of $f(T)$ Gravity
• Noether Symmetry Approach in $f(T,B)$ teleparallel cosmology
• Anisotropic Universe Models in f(T) Gravity
• Cosmological applications of $F(T,T_G)$ gravity
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• New classes of modified teleparallel gravity models
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• Remnant group of local Lorentz transformations in f(T) theories
• Stability of the flat FLRW metric in $f(T)$ gravity
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• Model-independent limits and constraints on extended theories of gravity from cosmic reconstruction techniques
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• Nonlocal Teleparallel Cosmology
• Geodesic Deviation Equation in $f(T)$ gravity
• McVittie solution in f(T) gravity
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• Brane cosmology in teleparallel and $f(T)$ gravity
• Action functional of the Cardassian universe