Geometric and physical characterizations of a spacetime concerning a novel curvature tensor

Abstract

In this article, we introduce $\Psi$-concircular curvature tensor, a new tensor that generalizes the concircular curvature tensor. At first, we produce a few fundamental geometrical properties of $\Psi$-concircular curvature tensor and pseudo $\Psi$-concircularly symmetric manifolds and provide some interesting outcomes. Besides, we investigate $\Psi$-concircularly flat spacetimes and establish some significant results about Minkowski spacetime, RW-spacetime, and projective collineation. Moreover, we show that if a $\Psi$-concircularly flat spacetime admits a Ricci bi-conformal vector field, then it is either Petrov type N or conformally flat. Moreover, we consider pseudo $\Psi$ concircularly symmetric spacetime with Codazzi type of Ricci tensor and prove that the spacetime is of Petrov types $I$, $D$ or $O$ and the spacetime turns into a $RW$ spacetime. Also, we establish that in a pseudo $\Psi$ concircularly symmetric spacetime with harmonic $\Psi$-concircular curvature tensor, the semi-symmetric energy momentum tensor and Ricci semi-symmetry are equivalent. At last, we produce a non-trivial example to validate the existence of a $(\mathcal{PCS})_4$ manifold.