Nontrivial Minkowski backgrounds in f(T) gravity

Boosted and rotated tetrad backgrounds for the Minkowski space arc studied in f(T) gravity. We perform Lorentzian perturbations at first order around nontrivial backgrounds and show that some Lorentz modes can exhibit nontrivial dynamics and can propagate in time. This remarkable feature gives evidence of additional mode(s) in the Lorentzian sector which have no precedent in Lorentz-violating modified gravities; however, they can cast doubts onto even theoretical viability of these models.