Gradient solitons on twisted product manifolds and their applications in general relativity

Abstract

In this paper, first, we find the necessary and sufficient condition for a Riemannian manifold to be the locally warped product. Then we investigate the existence of different types of gradient solitons, such as gradient (almost) Yamabe soliton, conformal soliton and gradient Ricci soliton on the twisted product manifolds. We also study the concircular flatness condition on a twisted product and examine the Einstein-type relations on its base and fiber manifold. Moreover, we introduce the notions of twisted generalized Robertson-Walker spacetime and twisted standard static spacetime. We get an ordinary differential equation (ODE) that determines the twisting function of the former and the exact form of the twisting function for the latter one.