Spacetimes with Semisymmetric Energy-Momentum Tensor

The object of the present paper is to introduce spacetimes with semisymmetric energy-momentum tensor. At first we consider the relation R ( X , Y )⋅ T =0, that is, the energy-momentum tensor T of type (0,2) is semisymmetric. It is shown that in a general relativistic spacetime if the energy-momentum tensor is semisymmetric, then the spacetime is also Ricci semisymmetric and the converse is also true. Next we characterize the perfect fluid spacetime with semisymmetric energy-momentum tensor. Then, we consider conformally flat spacetime with semisymmetric energy-momentum tensor. Finally, we cited some examples of spacetimes admitting semisymmetric energy-momentum tensor.