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

In this paper, we characterize weakly Ricci-symmetric (shortly, (WRS) 4 ) spacetimes and their solutions in f (ℛ) -gravity. It is demonstrated that a (WRS) 4 spacetime represents a stiff matter fluid. In addition, we obtain that a conformally flat (WRS) 4 spacetime is a space of quasi-constant sectional curvature. Moreover, we establish that a Ricci symmetric (WRS) 4 spacetime represents a static spacetime. Finally, we investigate the effect of (WRS) 4 spacetime solutions in f (ℛ) -gravity. [ABSTRACT FROM AUTHOR]