Non-Riemannian Description of Robinson-Trautman Spacetimes in Brans-Dicke Theory Of Gravity

Abstract

The variational field equations of Brans-Dicke scalar-tensor theory of gravitation are given in a non-Riemannian setting in the language of exterior differential forms over 4-dimensional spacetimes. A conformally re-scaled Robinson-Trautman metric together with the Brans-Dicke scalar field are used to characterise algebraically special Robinson-Trautman spacetimes. All the relevant tensors are worked out in a complex null basis and given explicitly in an appendix for future reference. Some special families of solutions are also given and discussed.