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 four-dimensional spacetimes. A conformally resealed Robinson-Trautman metric together with the Brans-Dicke scalar field are used to characterize 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.