Impact of concircular curvature tensor in $f\left(\mathcal{R}^{\ast}\right)$-gravity

Abstract

This paper concerns with the characterization of a spacetime and $f\left(\mathcal{R}^{\ast}\right)$-gravity endowed with concircular curvature tensor. We prove that a concircularly flat perfect fluid spacetime is either a de-Sitter spacetime or locally isometric to Minkowski spacetime . Moreover, it is established that a perfect fluid spacetime admitting harmonic concircular curvature tensor represents a Robertson-Walker spacetime. Finally, we examine the impact of concircularly flat perfect fluid spacetime solutions in two forms of $f\left(\mathcal{R}^{\ast}\right)$-gravity.