Conformally Flat Pseudoprojective Symmetric Spacetimes in f (R, G) Gravity

Sufficient conditions on a pseudoprojective symmetric spacetime (PPS)(n) whose Ricci tensor is of Codazzi type to be either a perfect fluid or Einstein spacetime are given. Also, it is shown that a (PPS)(n) is Einstein if its Ricci tensor is cyclic parallel. Next, we illustrate that a conformally flat (PPS)(n) spacetime is of constant curvature. Finally, we investigate conformally flat (PPS)(4) spacetimes and conformally flat (PPS)(4) perfect fluids in f (R, G) theory of gravity, and amongst many results, it is proved that the isotropic pressure and the energy density of conformally flat perfect fluid (PPS)(4) spacetimes are constants and such perfect fluid behaves like a cosmological constant. Further, in this setting, we consider some energy conditions.