Curvature properties of Robinson–Trautman metric

The curvature properties of Robinson–Trautman metric have been investigated. It is shown that Robinson–Trautman metric is a Roter type metric, and in a consequence, admits several kinds of pseudosymmetric type structures such as Weyl pseudosymmetric, Ricci pseudosymmetric, pseudosymmetric Weyl conformal curvature tensor etc. Moreover, it is proved that this metric is a 2-quasi-Einstein, the Ricci tensor is Riemann compatible and its Weyl conformal curvature 2-forms are recurrent. It is also shown that the energy momentum tensor of the metric is pseudosymmetric and the conditions under which such tensor is of Codazzi type and cyclic parallel have been investigated. Finally, we have made a comparison between the curvature properties of Robinson–Trautman metric and Som–Raychaudhuri metric.