Characterizations of a spacetime admitting gradient Ricci-Yamabe solitons and f(R)-gravity

In the present paper, we investigate the classification of a spacetime admitting gradient Ricci-Yamabe solitons in special conditions. We acquire that such a spacetime obeying divergence-free Weyl tensor becomes a generalized Robertson-Walker spacetime as well as a static spacetime and the spacetime represents dark matter era. Also, we show that such a spacetime is a Robertson-Walker spacetime and it is of Petrov type “O”. Moreover, it has also been investigated under what conditions this spacetime turns into a stiff matter era. In the last section of this paper, we examine the effect of this spacetime under f(R)-gravity scenario and derive several energy conditions graphically using two different models.