Comprehensive quasi-Einstein spacetime with application to general relativity

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