Cylindrically symmetric solutions in Einstein–Schrödinger theory

A specific cylindrically symmetric solution of Einstein–Schrödinger’s unified field theory is obtained in the electric, magnetic, and electromagnetic cases separately. The latter case is characterized by the use of Klotz’ metric hypothesis. By analyzing the geodesic equations, we determine the law of motion of a test particle within the field produced by the cylindrical charge source. The consequences of this study are (i) the source distribution is massless and (ii) the expansion of the source-particle universe does not result only from the cosmological constant of Einstein–Schrödinger’s unified theory but also from the existing charges. Possible connections to quantum field theory and the Yukawa potential are examined.