On Gradient Ricci-Yamabe Solitons

Abstract

In this paper, we establish some necessary and sufficient conditions for multiply warped product manifolds admitting a gradient Ricci-Yamabe soliton. For this purpose, the potential function of this soliton and the conditions that must be satisfied for each component of the multiply warped product manifold are investigated. As physical applications, multiply generalized Robertson–Walker spacetimes and generalized Reissner-Nordström spacetimes are discussed and results regarding the existence of gradient Ricci-Yamabe solitons on them are obtained.