Towards the Einstein-Hilbert action via conformal transformation

Physics

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

Scientific paper

A conformal transformation is used to prove that a general theory with the action S=FdDx √-g [F(φ,R)-(ɛ/2)(∇φ)2], where F(φ,R) is an arbitrary function of a scalar φ and a scalar curvature R, is equivalent to a system described by the Einstein-Hilbert action plus scalar fields. This equivalence is a simple extension of those in R2-gravity theory and the theory with nonminimal coupling. The case of F=L(R), where L(R) is an arbitrary polynomial of R, is discussed as an example.

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