Solutions of the nonsymmetric unified field theory

Abstract

The field equations in a formulation of Einstein's nonsymmetric unified field theory are solved exactly for the case of a static, spherically symmetric point singularity. The equations also yield the correct equations of motion in the lowest nontrivial order of approximation using the methods of Einstein, Infeld, and Hoffmann. When a universal constant $k$ vanishes, the theory reduces to the Einstein-Maxwell equations and the solution found here becomes the Reissner-Nordstr\"om solution. A coordinate singularity occurs in the metric when $r=m+{({m}^{2}\ensuremath{-}\frac{{Q}^{2}}{2})}^{\frac{1}{2}}$, as in the Reissner-Nordstr\"om solution. It is shown that this singularity is due to the choice of coordinates by performing a Kruskal-Szerkeres-type transformation. Further, the exact solutions which are generated by a Hermitian tensor, rather than a real nonsymmetric tensor, are given. Finally, the gauge invariance and possible renormalization of the theory are discussed.