Geometric classification of the torsion tensor of space-time

Torsion appears in literature in quite different forms. Generally. spin is considered to be the source of torsion, but there are several other possibi lities in which torsion emerges in different contexts. In some cases a phen omenological counterpart is absent, in some other cases torsion arises from sources without spin as a gradient of a scalar field. Accordingly, we prop ose two classification schemes. The first one is based on the possibility t o construct torsion tensors from the product of a covariant bivector and a vector and their respective space-time properties. The second one is obtain ed by starting from the decomposition of torsion into three irreducible pie ces. Their space-time properties again lead to a complete classification. T he classifications found are given in a U-4, a four dimensional space-time where the torsion tensor, have some peculiar properties. The irreducible de composition is useful since most of the phenomenological work done for tors ion concerns four dimensional cosmological models. In the second part of th e paper two applications of these classification schemes are given. The mod ifications of energy-momentum tensors are considered that arise due to diff erent sources of torsion. Furthermore, we analyze the contributions of tors ion to shear, vorticity, expansion and acceleration. Finally the generalize d Raychaudhuri equation is discussed.