Existence and Physical Properties of Gradient Ricci–Yamabe Solitons

Abstract

Wefirst prove the existence of the gradient Ricci–Yamabe soliton (brieflyGRYS)bycon-structing an explicit example endowed with the Robertson–Walker metric.Then we focus on thephysical properties of the gradient Ricci–Yamabe solitons satisying Einstein’sfield equations, under theassumptions of different subspaces of Gray’s decompositions. For instance, we prove that if a GRYS space-time satisfying Einstein’sfield equations, in which the gradient of the potential functionψis a unit-timeliketorse-forming vectorfield, belongs to the subspacesBandB′, then it is a Robertson–Walker space-timewith vanishing shear and vorticity. Moreover, its possible local cosmological structures are of Petrov types I,D, or O. Finally, we obtain the equations of state of a perfect-fluid space-time admitting the GRYS whosevelocityfield is a unit-timelike Killing vectorfield.