Perfect fluid spacetimes, Gray's decomposition and f(R, T)-gravity

In this paper, first we give the complete classifications of perfect fluid spacetimes under the Gray's decomposition. Then we investigate the condition under which the Ricci tensor is a conformal Killing tensor in a perfect fluid spacetime. Later, we study perfect fluid spacetimes in f (A, T)-gravity theory. We find some relations between isotropic pressure and energy density of the Ricci semisymmetric perfect fluid spacetimes satisfying f (A, T)- gravity equation to represent dark matter era.