Boosted and rotated tetrad backgrounds for the Minkowski space are studied in $f(\mathbb{T})$ 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.

• Received 12 December 2020
• Accepted 17 January 2021

DOI:https://doi.org/10.1103/PhysRevD.103.044009