On Ricci Symmetric Generalized Quasi Einstein Spacetimes

OpenAlex İngilizce

The object of the present paper is to prove the existence of a generalized quasi Einstein spacetime, briefly G.QE/ 4 , by constructing a non-trivial Lorentzian metric and to study such spacetime. First, we prove that every W 2 -Ricci pseudosymmetric G.QE/ 4 is an N.k/-quasi Einstein spacetime which can be considered as a model of perfect fluid, in general relativity. Then, we consider Ricci symmetric G.QE/ 4 and we prove that in such spacetime satisfying Einstein's field equations, the energy density and the isotropic pressure are constants. As a consequence of this result, the expansion scalar and the acceleration vector vanish and also the possible local cosmological structures of this spacetime obeying Einstein's field equations are of Petrov I, D or O.