Abstract
The purpose of this research is to investigate how a rho-Einstein soliton structure on a warped product manifold affects its base and fiber factor manifolds. Firstly, the pertinent properties of rho-Einstein solitons are provided. Secondly, numerous necessary and sufficient conditions of a rho-Einstein soliton warped product manifold to make its factor rho-Einstein soliton are examined. On a rho-Einstein gradient soliton warped product manifold, necessary and sufficient conditions for making its factor rho-Einstein gradient soliton are presented. rho-Einstein solitons on warped product manifolds admitting a conformal vector field are also considered. Finally, the structure of rho-Einstein solitons on some warped product space-times is investigated.