On a type of spacetimes

Abstract

In the present paper we characterize a type of spacetimes, called almost pseudo Z-symmetric spacetimes A(PZS) 4. At first, we obtain a condition for an A(PZS) 4 spacetime to be a perfect fluid spacetime and Roberson-Walker spacetime. It is shown that an A(PZS) 4 spacetime is a perfect fluid spacetime if the Z tensor is of Codazzi type. Next we prove that such a spacetime is the Roberson-Walker spacetime and can be identified with Petrov types I, D or O[3], provided the associated scalar φ is constant. Then we investigate A(PZS) 4 spacetimes satisfying divC = 0 and state equation is derived. Also some physical consequences are outlined. Finally, we construct a metric example of an A(PZS) 4 spacetime.