Methods for deriving solutions in generalized theories of gravitation: The Einstein-Cartan theory

In relativistic theories of gravitation that use, besides the metric, additional geometric objects in the description of the gravitational field, there exist two ways to obtain simplifying assumptions. One is to use symmetries of the geometric objects involved and the other is to use their a prior physical role. However, these two methods are related via the field equations; thus an arbitrary selection of simplifying assumptions may be inconsistent. We illustrate this point in the Einstein-Cartan theory and show that (a) under a certain assumption well-known solutions of this theory use incompatible simplifying assumptions and (b) a new solution which is compatible with the cosmological principle, and for which torsion cannot represent spin, exists.