Solutions of the Field Equations and Possible Meaning of the Hermitian Theory of Relativity

Abstract

A b s t r a c t. 'A procedure is stated, which allows to build solutions of ;the Hermitian theory of relativity from known solutions of the general theory of relativity.Solutions depending on three co-ordinates, built from Minkowski metric, as well as Hermitian generalizations of the Weyl-Levi Civita solution are shown. They suggest that the imaginary part of the fundamental tensor gik may encompass fields of different physical behaviour, like the electromagnetic field and a field responsible for forces which do not depend on the distance between charges which cannot exist as individuals.

Electrostatics and Confinement in Einstein's Unified Field Theory

“…The same conclusion can be drawn also with an argument that relies on another exact solution [34] belonging to the class described in [19]. The solution is a Hermitian generalization of the Curzon metric [35].…”

“…There is however an opportunity for defining these four-currents in a non phenomenological manner, that has been overlooked up to now. Let C pqik be Weyl's conformal curvature tensor [21] built with Hély's metric s ik , and already quoted in equation (34) of [22]. In Einstein's unified field theory Petrov eigenvalue equation [23] is naturally found to read: (6.1)…”

“…In the mentioned paper[34], the deviation from the elementary flatness was calculated by availing of g (ik) as metric. The calculation was repeated with the right metric s ik , and has provided just the same result.…”