Pseudo Generalized Quasi-Einstein Manifolds with Applications to General Relativity

Abstract

Quasi-Einstein manifold and generalized quasi-Einstein manifold are the generalization of Einsteinmanifold. In the present paper we discuss about a set of some geometric properties of pseudo generalized quasi-Einstein manifold and we give three and four examples (both Riemannian and Lorentzian) of pseudo generalized quasi-Einstein manifold to show the existence of such manifold. We also discuss PG(QE)4 spacetimewith space-matter tensor and some properties related to it. Lastlywe prove the existence of a pseudo generalized quasi-Einstein spacetime by constructing a non-trivial example.