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

TL;DR

This paper reformulates Brans-Dicke gravity in a non-Riemannian framework using differential forms, characterizing Robinson-Trautman spacetimes with explicit tensor calculations and special solutions.

Contribution

It introduces a non-Riemannian variational formulation of Brans-Dicke theory and explicitly characterizes Robinson-Trautman spacetimes within this setting.

Findings

Explicit tensor expressions for Robinson-Trautman spacetimes

Characterization of algebraically special solutions

Discussion of special solution families

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.