Degrees of freedom of $f(T)$ gravity

Abstract

We investigate the Hamiltonian formulation of $f(T)$ gravity and find that there are five degrees of freedom. The six first class constraints corresponding to the local Lorentz transformation in Teleparallel gravity become second class constraints in $f(T)$ gravity, which leads to the appearance of three extra degrees of freedom and the violation of the local Lorentz invariance in $f(T)$ gravity. In general, there are $D-1$ extra degrees of freedom for $f(T)$ gravity in $D$ dimensions, and this implies that the extra degrees of freedom correspond to one massive vector field or one massless vector field with one scalar field.

arXiv comment18 pages, some references added, minor revision to appear in JHEP

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Cited by in corpus (165)

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• Teleparallel Theories of Gravity: Illuminating a Fully Invariant Approach
• Reconstruction of $f(T)$ gravity: Rip cosmology, finite-time future singularities and thermodynamics
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• $f(T,\mathcal{T})$ gravity and cosmology
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• Nonminimal torsion-matter coupling extension of f(T) gravity
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• Observational Constraints on Teleparallel Dark Energy
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• Anisotropic Universe Models in f(T) Gravity
• Noether symmetries and analytical solutions in f(T)-cosmology: A complete study
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• Violation of the first law of black hole thermodynamics in $f(T)$ gravity
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