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On the Motion of Matter in Spacetime

T. Dereli·R. W. Tucker
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Abstract

We argue that the geodesic hypothesis based on auto-parallels of the Levi-Civita connection may need refinement in theories of gravity with additional scalar fields. This argument is illustrated with a re-formulation of the Brans-Dicke theory in terms of a spacetime connection with torsion determined dynamically in terms of the gradient of the Brans-Dicke scalar field. The perihelion shift in the orbit of Mercury is calculated on the alternative hypothesis that its world-line is an auto-parallel of such a connection. If scalar fields couple significantly to matter and spinless test particles move on such world-lines, current time keeping methods based on the conventional geodesic hypothesis may need refinement.

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T. Dereli, R. W. Tucker. 2001-07-05. On the Motion of Matter in Spacetime. https://arxiv.org/abs/gr-qc/0107017

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