On a type of spacetime

Abstract

The object of the present paper is to study a special type of spacetime. It is proved that in a conformally flat (W RS)4 spacetime with non-zero scalar curvature the vector field p defined by ɡ(X, p) = E(X) is irrotational and the integral curves of the vector field are geodesics. We also show that a conformally flat (W RS)4 spacetime with non-zero scalar curvature is the Robertson-Walker spacetime. Next possible local cosmological structure of such a spacetime is determined. Finally, we construct an example of a conformally flat (W RS)4 space-time with non-zero scalar curvature.

Keywords

• Weakly Ricci symmetric manifold
• weakly Ricci symmetric spacetime
• conformally flat weakly Ricci symmetric spacetime
• Robertson-Walker space-time
• weyl conformal curvature tensor
• conformally flat weakly Ricci symmetric perfect fluid spacetime
• energy-mome