Characterizations of a spacetime admitting $\Psi$-conformal curvature tensor

Abstract

In this paper, we introduce $\Psi$-conformal curvature tensor, a new tensor that generalizes the conformal curvature tensor. At first, we deduce a few fundamental geometrical properties of $\Psi$-conformal curvature tensor and pseudo $\Psi$-conharmonically symmetric manifold and produce some interesting outcomes. Moreover, we study $\Psi$-conformally flat perfect fluid spacetimes. As a consequence, we establish a number of significant theorems about radiation era, Minkowski spacetime, GRW-spacetime, projective collineation. Moreover, we show that if a $\Psi$-conformally flat spacetime admits a Ricci bi-conformal vector field, then it is either conformally flat or of Petrov type N. At last, we consider pseudo $\Psi$ conformally symmetric spacetime admitting harmonic $\Psi$-conformal curvature tensor and prove that the semi-symmetric energy momentum tensor and Ricci semi-symmetry are equivalent and also, the Ricci collineation and matter collineation are equivalent.