On Pseudo $B$-symmetric spacetimes and $f(\mathcal{R})$ gravity

TL;DR

This paper characterizes pseudo B-symmetric spacetimes, shows their relation to perfect fluid and Robertson-Walker models, and explores their behavior under a specific f(R) gravity model with energy conditions.

Contribution

It introduces a new characterization of pseudo B-symmetric spacetimes, links them to perfect fluids and Robertson-Walker models, and analyzes their properties within a novel f(R) gravity framework.

Findings

Pseudo B-symmetric spacetimes can be perfect fluid spacetimes.

Such spacetimes are conformally flat and resemble Robertson-Walker models.

The study derives energy conditions for a new f(R) gravity model.

Abstract

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 $\varPsi (t)$ 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 $f\left(\mathcal{R}\right)= e^{(\alpha \mathcal{R})}-ln(\beta \mathcal{R})$ in which $\alpha$ and $\beta$ are positive constants.