On pseudo B-symmetric spacetimes and f(ℛ) gravity

Abstract

This paper delivers the characterization of a pseudo [Formula: see text]-symmetric spacetimes and we illustrate that a pseudo [Formula: see text]-symmetric spacetime admitting Codazzi type of [Formula: see text]-tensor represents a perfect fluid spacetime and if this spacetime admits the time-like convergence criterion, then the pseudo [Formula: see text]-symmetric spacetime fulfills cosmic strong energy criterion and contains pure matter. Besides, we find in a pseudo [Formula: see text]-symmetric spacetime with Codazzi type of [Formula: see text]-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 [Formula: see text]-tensor is conformally flat and represents a Robertson–Walker spacetime. Also, we calculate the scale factor [Formula: see text] for these spacetimes in a spatially flat Robertson–Walker spacetime. Finally, we study the impact of this spacetime under [Formula: see text] gravity scenario and deduce several energy conditions by considering a new model [Formula: see text] in which [Formula: see text] and [Formula: see text] are positive constants.