MMN-1447
On Ricci symmetric generalized quasi Einstein spacetimes
Abstract
The object of the present paper is to prove the existence of the generalized quasi Einstein spacetime, denoted by G(QE)_4,by constructing the non-trivial Lorentzian metric and study on such spacetime. Then we proved that this spacetime satisfying the condition W_2\cdot S = L_SQ(g;S), where Q(g;S) denotes the Tachibana tensor, is an N(\frac{a-b}{3})-quasi Einstein spacetime. Consequently, this spacetime with the condition
W_2\cdot S = 0 can be considered as a model of perfect
fluid, in general relativity. Later, we consider Ricci symmetric G(QE)_4 and we prove that in such spacetime
satisfying Einstein's field equation, the energy density and the isotropic pressure are constants and the expansion scalar and the acceleration vector
vanish, also the possible local cosmological structures of this spacetime obeying the Einstein's eld equation are of Petrov I, D or O.
Vol. 16 (2015), No. 2, pp. 853-868