The $W$-curvature tensor on relativistic space-times

Abstract

This paper aims to study the W * −curvature tensor on relativistic space-times. The energy-momentum tensor T of a space-time is semisymmetric given that the W ⋆ −curvature tensor is semi-symmetric whereas energy-momentum tensor T of a space-time having a divergence free W ⋆ −curvature tensor is of Codazzi type. A space-time having a traceless W * −curvature tensor is Einstein. A W * −curvature flat space-time is Einstein. Perfect fluid space-times which admits W ⋆ −curvature tensor are considered.