On a Type of Spacetime
Mathematica Moravica, Tome 18 (2014) no. 1.

Voir la notice de l'article dans eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

The object of the present paper is to study a special type of spacetime. It is proved that in a conformally flat $(WRS)$_{4}$ spacetime with non-zero scalar curvature the vector field $\rho$ defined by $ɡ(X,\rho) = E(X)$ is irrotational and the integral curves of the vector field $\rho$ are geodesics. We also show that a conformally flat $(WRS)_{4}$ 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 $(WRS)_{4}$ space-time with non-zero scalar curvature.
Mots-clés : Weakly Ricci symmetric manifold, weakly Ricci symmetric spacetime, conformally flat weakly Ricci symmetric spacetime, Robertson-Walker spacetime, weyl conformal curvature tensor, conformally flat weakly Ricci symmetric perfect fluid spacetime, energy-momentum tensor 
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Sahanous Mallick; Uday C; and De. On a Type of Spacetime. Mathematica Moravica, Tome 18 (2014) no. 1. https://geodesic-test.mathdoc.fr/item/MM3_2014_18_1_a3/