A Study On Some Geometric Properties and Physical Applications of A Mixed Quasi-Einstein Spacetime

Abstract

In the present paper we discuss about a set of geometric properties and physical applications of a mixed quasi-Einstein spacetime[M (QE) 4 ], which is a special type of nearly quasi-Einstein spacetime[N (QE) 4 ]. Firstly we consider a nearly quasi-Einstein manifold[N (QE) n ] along with a mixed quasi-Einstein manifold[M (QE) n ] and study some geometric conditions with respect to different curvature tensors on them. Then we consider a mixed quasi-Einstein spacetime and study W 2 -Ricci pseudosymmetry and projective Ricci pseudosymmetry on it. Then we study the conditions H • S = 0 and C • S = 0 in an M (QE) 4 spacetime, where H, C are the conharmonical curvature tensor and semiconformal curvature tensor respectively. Next we consider a semiconformally flat Ricci pseudosymmetric M (QE) 4 spacetime and find the nature of that spacetime. In the next section we study about some applications of a perfect fluid M (QE) 4 spacetime in the general theory of relativity. Followed by we discuss about the Ricci soliton structure in a semiconformally flat M (QE) 4 spacetime satisfying Einstein field equation without cosmological constant. Finally we give a nontrivial example of a M (QE) 4 spacetime to establish the existence of it.