A Study of Generalized Quasi Einstein Spacetimes with Applications in General Relativity

The aim of this paper is to investigate some geometric and physical properties of the generalized quasi Einstein spacetime G(QE)₄ under certain conditions. Firstly, we prove the existence of G(QE)₄ by constructing a non trivial example. Then it is proved that the G(QE)₄ spacetime with the conditions ℬ⋅S=LSQ(g,S)$\mathcal {B}\cdot S=L_{S}Q(g,S)$, where ℬ$\mathcal {B}$ denotes the Ricci tensor or the concircular curvature tensor is an N(a−b3)$N(\frac {a-b}{3})$-quasi Einstein spacetime and in a G(QE)₄ spacetime with C ⋅ S = 0, where C is the conformal curvature tensor, a − b is an eigenvalue of the Ricci operator. Then, we deal with the Ricci recurrent G(QE)₄ spacetime and prove that in this spacetime, the acceleration vector and the vorticity tensor vanish; but this spacetime has the non-vanishing expansion scalar and the shear tensor. Moreover, it is shown that every Ricci recurrent G(QE)₄ is Weyl compatible, purely electric spacetime and its possible Petrov types are I or D.