The Existence of Gradient Yamabe Solitons on Spacetimes

Abstract

The main aim of the present article is to study generalized quasi-Yamabe gradient solitons on warped product manifolds. First, we obtain some necessary and sufficient conditions for the existence of generalized quasi-Yamabe gradient solitons equipped on a warped product structure. Then we study some important applications in the Lorentzian and the neutral settings for the particular class, called as gradient Yamabe soliton. More explicitly, we prove the existence of the non-trivial gradient Yamabe soliton on generalized Robertson–Walker spacetimes, standard static spacetimes, Walker manifolds and pp-wave spacetimes.