Comprehensive quasi-Einstein spacetime with application to general relativity (2105.08010v2)

Abstract: The aim of this paper is to extend the notion of all known quasi-Einstein manifolds like generalized quasi-Einstein, mixed generalized quasi-Einstein manifold, pseudo generalized quasi-Einstein manifold and many more and name it comprehensive quasi Einstein manifold C(QE)${n}$. We investigate some geometric and physical properties of the comprehensive quasi Einstein manifolds C(QE)${n}$ under certain conditions. We study the conformal and conharmonic mappings between C(QE)${n}$ manifolds. Then we examine the C(QE)${n}$ with harmonic Weyl tensor. We investigate geometric and physical properties of the comprehensive quasi Einstein manifolds C(QE)${n}$ under certain conditions. We define the manifold of comprehensive quasi-constant curvature and proved that conformally flat C(QE)${n}$ is manifold of comprehensive quasi-constant curvature and vice versa. We study the general two viscous fluid spacetime C(QE)${4}$ and find out some important consequences about C(QE)${4}$. We study C(QE)$_{n}$ with vanishing space matter tensor. Finally, we prove the existence of such manifolds by constructing non-trivial example.