On existence of a possible Lorentz invariant modified gravity in Weitzenböck spacetime

Abstract

Modified gravity which was constructed by torsion scalar $T$, namely $f(T)$ doesn't respect Lorentz symmetry. As an attempt to make a new torsion based modified gravity with Lorentz invarianve, recently $f(T,\mathcal{B})$ introduced where $B=2{\nabla }_{\mu }{T}^{\mu }$ \citep{Bahamonde:2015zma}. We would argue, even when all is constructed and done in a self-consistent form, if you handle them properly,we observe that there is no Lorentz invariant teleparallel equivalent of $f(R)$ gravity. All we found is that the $f(R)$ gravity in which $R$ must be computed in Weitzenböck spacetime, using Weitzenböck's connection, nor Levi-Civita connections is the only possible Lorentz invariant type of modified gravity. Consequently, $f(T)$ gravity can not obey Lorentz symmetry not only in its orthodoxica form but even in this new framework $f(T,\mathcal{B})$.

http://link.springer.com/article/10.1007%2Fs10509-015-2546-6

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• On spherically symmetric vacuum solutions and horizons in covariant $f(T)$ gravity theory
• Charged Black Holes with Yukawa Potential
• Regular solutions in $f(T)$-Yang-Mills theory
• Analytical Stellar Models of Neutron Stars in Teleparallel Gravity
• Symmetry and Conserved Quantities in $f(R)$-Gravity: Mei vs. Noether Approaches
• Noether symmetry in $F(T)$ gravity with $f$-essence