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 RobersonWalker 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 as Petrov types I, D or O[3], provided the associated scaler 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.