A note on generalized Robertson-Walker spacetimes and f(R*)-gravity

First, we prove that a Ricci symmetric spacetime is a perfect fluid spacetime if and only if it is a generalized Robertson-Walker spacetime. Consequently, we establish that under certain constraints on the associated scalar, such a spacetime turns into a static spacetime and is classified under Petrov classification I, D, or O. Also, we notice that a semi-symmetric as well as pseudo-Ricci symmetric generalized Robertson-Walker spacetime is a perfect fluid spacetime. We examine conformally flat generalized Robertson-Walker spacetime as a solution of f(R*)-gravity theory and describe the physical relevance. For the model f(R*) = ln(R*) - exp(-R*), numerous energy conditions in terms of associated scalars are investigated. This model agrees with the current investigations which states that the Cosmos is in an accelerating phase.