A study of almost pseudo symmetric spacetimes with application to f (R) gravity.

We prove that an almost pseudo symmetric spacetime with Codazzi type of tensor is perfect fluid whose velocity vector field B i is parallel. The energy density σ of such perfect fluid spacetime is constant and the state equation is obtained. Also, this spacetime is shown to be a static spacetime. Next, it is shown that such spacetime is a GRW spacetime with Einstein fiber. This kind of spacetime is investigated in f (R) theory of gravity; in this case, we find the forms of the isotropic pressure p and the energy density σ which are constant. Further, some energy conditions are studied in this spacetime. Finally, a concrete example of almost pseudo symmetric spacetimes is considered. [ABSTRACT FROM AUTHOR]