Abstract
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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This work was done in the sphere of activity of the C.N.R. Groups for mathematical research.
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Udeschini, E.B. A natural scalar field in the einstein gravitational theory. Gen Relat Gravit 12, 429–437 (1980). https://doi.org/10.1007/BF00756174
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DOI: https://doi.org/10.1007/BF00756174