Absence of Relativistic Stars in f(T) Gravity

In this work we investigate the structure of neutron stars in modified f(T) gravity models. We find that, unlike the f(R) models, the equations of motion put a rather strict constraint on the possible f(T) functions. Specifically, after analyzing the problem in two different choice of coordinates with spherical symmetry, we conclude that the relativistic neutron star solution in f(T) gravity models is possible only if f(T) is a linear function of the torsion scalar T, that is in the case of Teleparallel Equivalent of General Relativity.