Abstract
In the framework of Einstein-Cartan (EC) theory, the Brans-Dicke (BD) theory is considered and it is found that a scalar field nonminimally coupled to the gravitational field gives rise to torsion, even though the scalar field has zero spin. The metric equations stay the same if the coupling constant is rescaled, but the equations of motion of a test particle, derived from the conservation equations, differ from those of the usual BD theory without torsion. The gravitational red-shift value differs considerably from the usual prediction of general theory of relativity (GTR), and rules out the possibility of a torsion version of BD theory forω<6.
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Jha, R., Lord, E.A. & Sinha, K.P. The Brans-Dicke scalar field in Einstein-Cartan theory. Gen Relat Gravit 20, 943–950 (1988). https://doi.org/10.1007/BF00760092
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DOI: https://doi.org/10.1007/BF00760092