On Conformally Flat Almost Pseudo-Ricci Symmetric Spacetimes

Abstract

We consider a conformally flat almost pseudo-Ricci symmetric spacetime. At first we show that a conformally flat almost pseudo-Ricci symmetric spacetime can be taken as a model of the perfect fluid spacetime in general relativity and cosmology. Next we show that if in a conformally flat almost pseudo-Ricci symmetric spacetime the matter distribution is perfect fluid whose velocity vector is the vector field corresponding to 1-form B of the spacetime, the energy density and the isotropic pressure are not constants. We also show that a conformally flat almost pseudo-Ricci symmetric spacetime is the Robertson-Walker spacetime. Finally we give an example of a conformally flat almost pseudo-Ricci symmetric spacetime with non-zero non-constant scalar curvature admitting a concircular vector field.

A condition for a perfect-fluid space-time to be a generalized Robertson-Walker space-time

“…De and Ghosh [11] showed that if R ij = Ag ij + Bu i u j with u i closed and C ijkl = 0, then u is a concircular vector. The results were extended by Mantica et al to pseudo Z-symmetric spaces [24] and to weakly Z-symmetric spaces [25].…”

Curvature properties of some 4-dimensional semi-Riemannian metrics

“…, x 4 are the standard coordinates of R 4 . We note that such type of metric was first appeared in [89] and latter used by many authors (see [15,16,100]) to prove the existence of various curvature restricted geometric structures. This paper is organized as follows.…”

On Almost Pseudo Conharmonically Symmetric Manifolds

“…If in the above equation B = A, then the (AP S) n reduces to a(P S) n . In subsequent papers ( [11], [12]) De and Gazi studied almost pseudo conformally symmetric manifolds and conformally flat almost pseudo Ricci symmetric manifolds. It may be mentioned that (P S) n is a particular case of an (AP S) n , but(W S) n is not a particular case of an (AP S) n .…”