Conformally Flat Pseudoprojective Symmetric Spacetimes infR,GGravity

Abstract

Sufficient conditions on a pseudoprojective symmetric spacetime${\left(\text{PPS}\right)}_n$whose Ricci tensor is of Codazzi type to be either a perfect fluid or Einstein spacetime are given. Also, it is shown that a${\left(\text{PPS}\right)}_n$is Einstein if its Ricci tensor is cyclic parallel. Next, we illustrate that a conformally flat${\left(\text{PPS}\right)}_n$spacetime is of constant curvature. Finally, we investigate conformally flat${\left(\text{PPS}\right)}_4$spacetimes and conformally flat${\left(\text{PPS}\right)}_4$perfect fluids in$f\left(R,\mathcal{G}\right)$theory of gravity, and amongst many results, it is proved that the isotropic pressure and the energy density of conformally flat perfect fluid${\left(\text{PPS}\right)}_4$spacetimes are constants and such perfect fluid behaves like a cosmological constant. Further, in this setting, we consider some energy conditions.