On the detection of scalar field induced space-time torsion

Abstract

We argue that the geodesic hypothesis based on autoparallels of the Levi-Civita connection may need refinement in the scalar-tensor theories of gravity. Based on a reformulation of the Brans-Dicke theory in terms of a connection with torsion determined dynamically in terms of the gradient of the Brans-Dicke scalar field, we compute the perihelion shift in the orbit of Mercury on the alternative hypothesis that its worldline is an autoparallel of a connection with torsion. If the Brans-Dicke scalar field couples significantly to matter and test particles move on such worldlines, the current time keeping methods based on the conventional geodesic hypothesis may need refinement.