Does Brans-Dicke theory always yield general relativity in the infinite ω limit?

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Gravity In More Than Four Dimensions, Kaluza-Klein Theory, Unified Field Theories, Alternative Theories Of Gravity

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In this work it is shown that the Brans-Dicke theory of gravity does not always go over to general relativity in the ω-->α limit. It is also shown, by an order of magnitude estimate, that one can get general relativity as a limit of Brans-Dicke theory when ω-->α, only if the trace of the energy-momentum tensor describing all fields other than the Brans-Dicke scalar field is nonzero.

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