Ricci-Yamabe Solitons in f(R)-gravity
Krishnendu De, Uday Chand De
Abstract
The main objective of this paper is to describe the perfect fluid spacetimes fulfilling $f(R)$-gravity, when Ricci-Yamabe, gradient Ricci-Yamabe and $\eta$-Ricci-Yamabe solitons are its metrics. We acquire conditions for which the Ricci-Yamabe and the gradient Ricci-Yamabe solitons are expanding, steady or shrinking. Furthermore, we investigate $\eta$-Ricci-Yamabe solitons and deduce a Poisson equation and with the help of this equation, we acquire some significant results.
Topics & Concepts
Yamabe flowRicci flowRicci curvaturePhysicsMathematicsMathematical physicsMathematical analysisScalar curvatureGeometryCurvatureSectional curvatureAdvanced Differential Geometry ResearchGeometric Analysis and Curvature FlowsCosmology and Gravitation Theories