Generalized concircular curvature tensor and Spacetimes of general relativity

Abstract

In This paper, we introduced a new tensor named generalized concircular curvature tensor on a Riemannian manifold which generalized the concircular curvature tensor. First, we deduced some basic geometric properties of generalized concircular curvature tensor. Further, a symmetric investigation of generalized concircular curvature tensor has been made on the four-dimensional spacetime of general relativity. The spacetime fulfilling Einstein field equations with the vanishing of generalized concircular curvature tensor is being considered and the existence of killing and Conformal killing vectors on such spacetime have been established. At last, we extend the similar case for the investigation of cosmological models with dust and perfect fluid spacetime.