Perfect fluid spacetimes, Gray's decomposition and $f(\mathcal{R}, {T})$-gravity

Abstract

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 $f(\mathcal{R},T)$-gravity theory. We find some relations between isotropic pressure and energy density of the Ricci semisymmetric perfect fluid spacetimes satisfying $f(\mathcal{R},T)$-gravity equation to represent dark matter era.