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.

Automated summary

The article provides sufficient conditions for a pseudoprojective symmetric spacetime with Ricci tensor of Codazzi type to be either a perfect fluid or Einstein spacetime. It is also shown that a pseudoprojective symmetric spacetime is Einstein if its Ricci tensor is cyclic parallel. Additionally, the article investigates the properties of conformally flat pseudoprojective symmetric spacetimes and conformally flat perfect fluids in the f (R, G) theory of gravity, obtaining various results including the constancy of isotropic pressure and energy density in conformally flat perfect fluid spacetimes.