We show that McVittie geometry, which describes a black hole embedded in a FLRW universe, not only solves the Einstein equations but also remains as a non-deformable solution of f(T) gravity. This search for GR solutions that survive in f(T) gravity is facilitated by a null tetrad approach. We also show that flat FLRW geometry is a consistent solution of f(T) dynamical equations not only for $$T=-6H^{2}$$ but also for $$T=0$$ , which could be a manifestation of the additional degrees of freedom involved in f(T) theories.

McVittie solution in f(T) gravity