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

Abstract

In this paper, we characterize weakly Ricci-symmetric (shortly, (WRS)4) spacetimes and their solutions in [Formula: see text]-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 [Formula: see text]-gravity.

Characterizations of vacuum solutions of f(R) − gravity in space-times admitting Z tensor of Codazzi type

“…Constant curvature solutions have been discovered in systems exhibiting cylindrical symmetry [29,30], planar symmetry [31], and local rotational symmetry [32]. We also note that the characterization of weakly Ricci-symmetric space-times and their solutions in f (R)-gravity were recently obtained in [33]. Inspired by these papers and numerous others, we direct our focus towards characterizing the vacuum solutions of f (R) − gravity in a space-time that possesses a Z tensor of Codazzi type.…”

“…The authors of [21] studied projectively flat space-times as a possible solution of f (R)-gravity, they proved that the matter field has constant energy density and isotropic pressure. In [22][23][24], investigation of certain space-times as a solutions of f (R)-gravity are investigated.…”