X iv : g r - qc / 0 41 11 19 v 1 2 5 N ov 2 00 4 On the teleparallel limit of Poincaré gauge theory

We will address the question of the consistency of teleparallel theories in presence of spinning matter which has been a controversial subject of discussion over the last twenty years. We argue that the origin of the problem is not simply the symmetry or asymmetry of the stress-energy tensor of the matter fields, which has been recently analyzed by several authors, but arises at a more fundamental level, namely from the invariance of the field equations under a frame change, a problem that has been discussed long time ago by Kopczynski in the framework of the teleparallel equivalent of general relativity. More importantly, we show that the problem is not only confined to the purely teleparallel theory but arises actually in every Poincaré gauge theory that admits a teleparallel geometry in the absence of spinning sources, i.e. in its classical limit. The reason for this is that the frame invariance, even though in most cases not a symmetry of the full gravitational Lagrangian, will rearise as a symmetry of the classical limit of the field equations. Since on the other hand, the matter fields in general do not present this symmetry, their behavior will remain partly unpredictable if treated as test matter on a classical background.