Ricci Solitons on Spacelike Hypersurfaces of Generalized Robertson-Walker Spacetimes

In this paper, we investigate Ricci solitons on spacelike hypersurfaces in a special Lorentzian warped product manifold, the so-called generalized Robertson-Walker (GRW) spacetimes. Such spacetimes admit a natural form of symmetry which is represented by the conformal vector field f partial derivative t, where f is the warping function and partial derivative t is the unit timelike vector field tangent to the base (which is here a one-dimensional manifold). We use this symmetry to introduce some fundamental formulas related to the Ricci soliton structures and the Ricci curvature of the fiber, the warping function, and the shape operator of the immersion. We investigate different rigidity results for Ricci solitons on the slices, in addition to the totally umbilical spacelike supersurfaces of GRW. Furthermore, our study is focused on significant GRW spacetimes such as Einstein GRW spacetimes and those which obey the well-known null convergence condition (NCC).