Some geometric and physical properties of generalized quasi-Einstein spacetimes and f(R) gravity

This paper examines the characterizations of generalized quasi-Einstein spacetimes in [Formula: see text] gravity. It is established that a Ricci-symmetric generalized quasi-Einstein spacetime is either Einsteinian, quasi-Einsteinian or static. It is demonstrated that a perfect fluid generalized quasi-Einstein spacetime represents radiation era under certain conditions. It is proven that a generalized quasi-Einstein GRW spacetime is a perfect fluid. The paper also reveals that the isotropic pressure and energy density of a perfect fluid generalized quasi-Einstein spacetime obeying [Formula: see text] gravity remain constant. Finally, the study explores various energy conditions.