On Pseudo B-Symmetric Spacetimes and f(ℛ) Gravity

This article delivers the characterization of a pseudo B symmetric spacetimes and we illustrate that a pseudo B symmetric spacetime admitting Codazzi type of B-tensor represents a perfect fluid spacetime and if this spacetime admits the time-like convergence criterion, then the pseudo B symmetric spacetime fulfills cosmic strong energy criterion and contains pure matter. Besides, we find in a pseudo B symmetric spacetime with Codazzi type of B-tensor the electric part of the Weyl tensor vanishes and has Riemann and Weyl compatible vector fields. Furthermore, it is established that the chosen spacetime with Codazzi type of B-tensor is conformally flat and represents a Robertson-Walker spacetime. Also, we calculate the scale factor (t) for these spacetimes in a spatially flat Robertson-Walker spacetime. Finally, we study the impact of this spacetime under $f(R)$ gravity scenario and deduce several energy conditions by considering a new model f(R)= e(α R)-ln(β R) in which α and β are positive constants.