Perfect fluid spacetimes obeying certain restrictions on the energy-momentum tensor


Krishnendu De, Udaj Chand De




This paper is concerned with the study of a perfect fluid spacetime endowed with the various forms of the energy-momentum tensor T. We establish that a perfect fluid spacetime endowed with covariant constant energy-momentum tensor represents a dark matter era or the matter content is a perfect fluid spacetime with vanishing vorticity; whereas a perfect fluid spacetime endowed with Codazzi type of T represents a dark matter era or the expansion scalar vanishes, provided α 1 remains invariant under the velocity vector field ρ. Also, we show that a perfect fluid spacetime with pseudo-symmetric energy-momentum tensor represents a dark matter era or a phantom era, provided the velocity vector field annihilates the curvature tensor. Moreover, we characterize T-recurrent and weakly-T symmetric perfect fluid spacetimes with Killing velocity vector field and acquired that the perfect fluid spacetimes represent a radiation era in the first case and a stiff matter for the last one.