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

We prove that an almost pseudo [Formula: see text] symmetric spacetime with Codazzi type of [Formula: see text] tensor is perfect fluid whose velocity vector field [Formula: see text] is parallel. The energy density [Formula: see text] 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 [Formula: see text] which are constant. Further, some energy conditions are studied in this spacetime. Finally, a concrete example of almost pseudo [Formula: see text] symmetric spacetimes is considered.