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

Abstract

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 $\alpha_1$ remains invariant under the velocity vector field $\rho$. 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 anihilates 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.