The meaning of torsion in teleparallel theories

The ambiguity of the Weitzenb & ouml;ck connection is investigated from the perspective of frames. In doing so, the pure-tetrad formalism and the formalism with an affine connection are compared with each other; it is shown that the ambiguity in the affine connection is equivalent to that of the frame. The role played by the regularization procedure is discussed, and it is argued that the frame approach gives better results than any regularization procedure, including those that make use of a suitable choice of the affine connection. It is also argued that, for consistency, the Weitzenb & ouml;ck torsion must be either manifesting only gravitational effects or gravitational effects plus accelerations. Two possible interpretations for the torsion tensor are present, and an application to a frame that accelerates along the same direction as that of a pp-wave is used to show the consistence of these interpretations. Finally, some possible solutions to the well-known problems of the f(T) theories are proposed.