A Study of Spacetimes with vanishing M−projective Curvature Tensor

Abstract

In this paper we study about the M−projectively flat perfect fluid spacetime. First of all we showed that the Riemannian curvature tensor of an M−projectively flat spacetime is covariantly constant. Then we found the length of the Ricci operator in an M−projectively flat perfect fluid spacetime and proved that the isotropic pressure and entry density of an M−projectively flat perfect fluid spacetime satisfying Einsteins field equation with cosmological constant are constant. Then we showed that an M−projectively flat perfect fluid spacetime satisfying Einsteins field equation with cosmological constant and obeying the timelike convergence condition has positive isotropic pressure. Further we showed that the isotropic pressure and the energy density of an M−projectively flat perfect fluid spacetime satisfying Einsteins field equation with cosmological constant vanishes in a purely electromagnetic distribution. Lastly we showed that an M−projectively flat perfect fluid spacetime with the energy momentum tensor of an electromagnetic field such that the spacetimesatisfies Einsteins field equation without cosmological constant is a Euclidean space