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Summary: arXiv:gr-qc/0405064v49Jun2005
THE ELECTROSTATICS OF EINSTEIN'S UNIFIED FIELD
THEORY
SALVATORE ANTOCI, DIERCK-EKKEHARD LIEBSCHER, AND LUIGI MIHICH
Abstract. When sources are added at their right-hand sides, and g(ik)
is a priori assumed to be the metric, the equations of Einstein's Hermit-
ian theory of relativity were shown to allow for an exact solution that
describes the general electrostatic field of n point charges. Moreover,
the injunction of spherical symmetry of g(ik) in the infinitesimal neigh-
bourhood of each of the charges was proved to yield the equilibrium
conditions of the n charges in keeping with ordinary electrostatics. The
tensor g(ik), however, cannot be the metric of the theory, since it enters
neither the eikonal equation nor the equation of motion of uncharged
test particles. A physically correct metric that rules both the behaviour
of wave fronts and of uncharged matter is the one indicated by H´ely.
In the present paper it is shown how the electrostatic solution pre-
dicts the structure of the n charged particles and their mutual posi-
tions of electrostatic equilibrium when H´ely's physically correct metric
is adopted.
1. Introduction
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