Conformally Flat Pseudoprojective Symmetric Spacetimes infR,GGravity

Abstract

Sufficient conditions on a pseudoprojective symmetric spacetime PPSnwhose Ricci tensor is of Codazzi type to be either a perfect fluid or Einstein spacetime are given. Also, it is shown that a PPSnis Einstein if its Ricci tensor is cyclic parallel. Next, we illustrate that a conformally flat PPSnspacetime is of constant curvature. Finally, we investigate conformally flat PPS4spacetimes and conformally flat PPS4perfect fluids infR,Gtheory of gravity, and amongst many results, it is proved that the isotropic pressure and the energy density of conformally flat perfect fluid PPS4spacetimes are constants and such perfect fluid behaves like a cosmological constant. Further, in this setting, we consider some energy conditions.