A natural scalar field in the einstein gravitational theory

Physics

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Scientific paper

In a Riemannian space-time, the difference between the third-order tensor potentialH αβλ of the Riemann tensor (presented in a precedent paper) and the Lanczos generating function of the Weyl tensor is here shown to be characterized by a vectorV α , obtained by contractionH αβλ . The significant role of such a vector, in the context of general relativity, is then discussed. Particular attention is paid to the scalar potential ϑ which characterizes the irrotational part ofV α : such a scalar field satisfies a space-time wave equation of the Poisson type. Weak fields are also considered: in the particular case of a static metric, the scalar ϑ is found to be proportional to the classic Newtonian potential.

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