Characterizations of weakly Ricci-symmetric spacetimes and f(ℛ)-gravity

Abstract

In this paper, we characterize weakly Ricci-symmetric (shortly, [Formula: see text]) spacetimes and their solutions in [Formula: see text]-gravity. It is demonstrated that a [Formula: see text] spacetime represents a stiff matter fluid. In addition, we obtain that a conformally flat [Formula: see text] spacetime is a space of quasi-constant sectional curvature. Moreover, we establish that a Ricci symmetric [Formula: see text] spacetime represents a static spacetime. Finally, we investigate the effect of [Formula: see text] spacetime solutions in [Formula: see text]-gravity.