Geometry of the statistical spacelike hypersurfaces of the GRW spacetimes

Abstract

We explore the geometry of the Generalized Robertson-Walker (GRW) spacetime under the assumption that it’s fiber is a statistical manifold. This approach allows us to endow a statistical structure on the GRW spacetime. Later, we derive necessary and sufficient conditions for the existence of a statistical Ricci soliton on the statistical spacelike hypersurface of a GRW spacetime. We explore the condition for a GRW spacetime to have an almost Ricci soliton structure, when the fiber of the GRW spacetime constitutes
a statistical Ricci soliton. Furthermore, we examine the case where both the fiber and the GRW spacetime are Ricci solitons, and we establish the necessary and sufficient conditions for the statistical spacelike
hypersurface to exhibit a Ricci soliton structure.